[{"data":1,"prerenderedAt":4923},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fquotientenregel":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fquotientenregel":4913},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":101,"checks":4854,"conditions":4873,"conditionsHtml":4874,"deprecated":4875,"description":4847,"extension":4876,"figure":4875,"figureCaption":4875,"figureHtml":4875,"formulaId":4877,"latex":4878,"latexHtml":4879,"level":4880,"meta":4881,"navigation":4882,"path":4883,"redirectFrom":4884,"related":4885,"seo":4889,"stem":4890,"subject":581,"summary":4891,"tags":4892,"variables":4897,"__hash__":4912},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fquotientenregel.md","Quotientenregel",[550,551,552,553,554],"Quotientenregel Ableitung","Bruch ableiten","NAZ minus ZAN durch N Quadrat","u durch v ableiten","Ableitung eines Quotienten",{"type":556,"value":557,"toc":4846},"minimark",[558,563,622,711,1106,1110,1244,2072,2131,2135,2720,3212,3721,4308,4312],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,570,571,617,618,621],"p",{},"Mit der ",[568,569,548],"strong",{}," leitet man Brüche ab, bei denen Zähler und Nenner von ",[572,573,576,598],"span",{"className":574},[575],"katex",[572,577,580],{"className":578},[579],"katex-mathml",[581,582,584],"math",{"xmlns":583},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[585,586,587,594],"semantics",{},[588,589,590],"mrow",{},[591,592,593],"mi",{},"x",[595,596,593],"annotation",{"encoding":597},"application\u002Fx-tex",[572,599,603],{"className":600,"ariaHidden":602},[601],"katex-html","true",[572,604,607,612],{"className":605},[606],"base",[572,608],{"className":609,"style":611},[610],"strut","height:0.4306em;",[572,613,593],{"className":614},[615,616],"mord","mathnormal"," abhängen. Eine bekannte Merkhilfe ist ",[568,619,620],{},"„NAZ minus ZAN durch N-Quadrat“",": Nenner mal Ableitung des Zählers minus Zähler mal Ableitung des Nenners, geteilt durch das Quadrat des Nenners.",[564,623,624,625,678,679,710],{},"Die Ableitung existiert nur dort, wo der Nenner ",[572,626,628,653],{"className":627},[575],[572,629,631],{"className":630},[579],[581,632,633],{"xmlns":583},[585,634,635,650],{},[588,636,637,640,645,647],{},[591,638,639],{},"v",[641,642,644],"mo",{"stretchy":643},"false","(",[591,646,593],{},[641,648,649],{"stretchy":643},")",[595,651,652],{"encoding":597},"v(x)",[572,654,656],{"className":655,"ariaHidden":602},[601],[572,657,659,663,667,671,674],{"className":658},[606],[572,660],{"className":661,"style":662},[610],"height:1em;vertical-align:-0.25em;",[572,664,639],{"className":665,"style":666},[615,616],"margin-right:0.0359em;",[572,668,644],{"className":669},[670],"mopen",[572,672,593],{"className":673},[615,616],[572,675,649],{"className":676},[677],"mclose"," nicht null ist. Diese Stellen gehören schon nicht zum Definitionsbereich von ",[572,680,682,696],{"className":681},[575],[572,683,685],{"className":684},[579],[581,686,687],{"xmlns":583},[585,688,689,694],{},[588,690,691],{},[591,692,693],{},"f",[595,695,693],{"encoding":597},[572,697,699],{"className":698,"ariaHidden":602},[601],[572,700,702,706],{"className":701},[606],[572,703],{"className":704,"style":705},[610],"height:0.8889em;vertical-align:-0.1944em;",[572,707,693],{"className":708,"style":709},[615,616],"margin-right:0.1076em;",".",[564,712,713,714,949,950,710],{},"Steht im Zähler nur eine Konstante, ist es oft einfacher, den Bruch als Potenz zu schreiben und die Potenzregel zu nutzen: ",[572,715,717,760],{"className":716},[575],[572,718,720],{"className":719},[579],[581,721,722],{"xmlns":583},[585,723,724,757],{},[588,725,726,741,744,746],{},[727,728,729,733],"mfrac",{},[730,731,732],"mn",{},"3",[734,735,736,738],"msup",{},[591,737,593],{},[730,739,740],{},"2",[641,742,743],{},"=",[730,745,732],{},[734,747,748,750],{},[591,749,593],{},[588,751,752,755],{},[641,753,754],{},"−",[730,756,740],{},[595,758,759],{"encoding":597},"\\frac{3}{x^2} = 3x^{-2}",[572,761,763,902],{"className":762,"ariaHidden":602},[601],[572,764,766,770,890,895,899],{"className":765},[606],[572,767],{"className":768,"style":769},[610],"height:1.1901em;vertical-align:-0.345em;",[572,771,773,777,887],{"className":772},[615],[572,774],{"className":775},[670,776],"nulldelimiter",[572,778,780],{"className":779},[727],[572,781,785,878],{"className":782},[783,784],"vlist-t","vlist-t2",[572,786,789,873],{"className":787},[788],"vlist-r",[572,790,794,847,858],{"className":791,"style":793},[792],"vlist","height:0.8451em;",[572,795,797,802],{"style":796},"top:-2.655em;",[572,798],{"className":799,"style":801},[800],"pstrut","height:3em;",[572,803,809],{"className":804},[805,806,807,808],"sizing","reset-size6","size3","mtight",[572,810,812],{"className":811},[615,808],[572,813,815,818],{"className":814},[615,808],[572,816,593],{"className":817},[615,616,808],[572,819,822],{"className":820},[821],"msupsub",[572,823,825],{"className":824},[783],[572,826,828],{"className":827},[788],[572,829,832],{"className":830,"style":831},[792],"height:0.7463em;",[572,833,835,839],{"style":834},"top:-2.786em;margin-right:0.0714em;",[572,836],{"className":837,"style":838},[800],"height:2.5em;",[572,840,844],{"className":841},[805,842,843,808],"reset-size3","size1",[572,845,740],{"className":846},[615,808],[572,848,850,853],{"style":849},"top:-3.23em;",[572,851],{"className":852,"style":801},[800],[572,854],{"className":855,"style":857},[856],"frac-line","border-bottom-width:0.04em;",[572,859,861,864],{"style":860},"top:-3.394em;",[572,862],{"className":863,"style":801},[800],[572,865,867],{"className":866},[805,806,807,808],[572,868,870],{"className":869},[615,808],[572,871,732],{"className":872},[615,808],[572,874,877],{"className":875},[876],"vlist-s","​",[572,879,881],{"className":880},[788],[572,882,885],{"className":883,"style":884},[792],"height:0.345em;",[572,886],{},[572,888],{"className":889},[677,776],[572,891],{"className":892,"style":894},[893],"mspace","margin-right:0.2778em;",[572,896,743],{"className":897},[898],"mrel",[572,900],{"className":901,"style":894},[893],[572,903,905,909,912],{"className":904},[606],[572,906],{"className":907,"style":908},[610],"height:0.8141em;",[572,910,732],{"className":911},[615],[572,913,915,918],{"className":914},[615],[572,916,593],{"className":917},[615,616],[572,919,921],{"className":920},[821],[572,922,924],{"className":923},[783],[572,925,927],{"className":926},[788],[572,928,930],{"className":929,"style":908},[792],[572,931,933,937],{"style":932},"top:-3.063em;margin-right:0.05em;",[572,934],{"className":935,"style":936},[800],"height:2.7em;",[572,938,940],{"className":939},[805,806,807,808],[572,941,943,946],{"className":942},[615,808],[572,944,754],{"className":945},[615,808],[572,947,740],{"className":948},[615,808],", also ",[572,951,953,997],{"className":952},[575],[572,954,956],{"className":955},[579],[581,957,958],{"xmlns":583},[585,959,960,994],{},[588,961,962,971,973,975,977,979,981,984],{},[734,963,964,966],{},[591,965,693],{},[641,967,970],{"mathvariant":968,"lspace":969,"rspace":969},"normal","0em","′",[641,972,644],{"stretchy":643},[591,974,593],{},[641,976,649],{"stretchy":643},[641,978,743],{},[641,980,754],{},[730,982,983],{},"6",[734,985,986,988],{},[591,987,593],{},[588,989,990,992],{},[641,991,754],{},[730,993,732],{},[595,995,996],{"encoding":597},"f'(x) = -6x^{-3}",[572,998,1000,1058],{"className":999,"ariaHidden":602},[601],[572,1001,1003,1007,1040,1043,1046,1049,1052,1055],{"className":1002},[606],[572,1004],{"className":1005,"style":1006},[610],"height:1.0019em;vertical-align:-0.25em;",[572,1008,1010,1013],{"className":1009},[615],[572,1011,693],{"className":1012,"style":709},[615,616],[572,1014,1016],{"className":1015},[821],[572,1017,1019],{"className":1018},[783],[572,1020,1022],{"className":1021},[788],[572,1023,1026],{"className":1024,"style":1025},[792],"height:0.7519em;",[572,1027,1028,1031],{"style":932},[572,1029],{"className":1030,"style":936},[800],[572,1032,1034],{"className":1033},[805,806,807,808],[572,1035,1037],{"className":1036},[615,808],[572,1038,970],{"className":1039},[615,808],[572,1041,644],{"className":1042},[670],[572,1044,593],{"className":1045},[615,616],[572,1047,649],{"className":1048},[677],[572,1050],{"className":1051,"style":894},[893],[572,1053,743],{"className":1054},[898],[572,1056],{"className":1057,"style":894},[893],[572,1059,1061,1065,1068,1071],{"className":1060},[606],[572,1062],{"className":1063,"style":1064},[610],"height:0.8974em;vertical-align:-0.0833em;",[572,1066,754],{"className":1067},[615],[572,1069,983],{"className":1070},[615],[572,1072,1074,1077],{"className":1073},[615],[572,1075,593],{"className":1076},[615,616],[572,1078,1080],{"className":1079},[821],[572,1081,1083],{"className":1082},[783],[572,1084,1086],{"className":1085},[788],[572,1087,1089],{"className":1088,"style":908},[792],[572,1090,1091,1094],{"style":932},[572,1092],{"className":1093,"style":936},[800],[572,1095,1097],{"className":1096},[805,806,807,808],[572,1098,1100,1103],{"className":1099},[615,808],[572,1101,754],{"className":1102},[615,808],[572,1104,732],{"className":1105},[615,808],[559,1107,1109],{"id":1108},"herleitung","Herleitung",[564,1111,1112,1113,1243],{},"Man bringt den Differenzenquotienten auf einen Nenner und ergänzt im Zähler ",[572,1114,1116,1166],{"className":1115},[575],[572,1117,1119],{"className":1118},[579],[581,1120,1121],{"xmlns":583},[585,1122,1123,1163],{},[588,1124,1125,1127,1130,1132,1134,1136,1138,1140,1142,1144,1147,1149,1151,1153,1155,1157,1159,1161],{},[641,1126,754],{},[591,1128,1129],{},"u",[641,1131,644],{"stretchy":643},[591,1133,593],{},[641,1135,649],{"stretchy":643},[591,1137,639],{},[641,1139,644],{"stretchy":643},[591,1141,593],{},[641,1143,649],{"stretchy":643},[641,1145,1146],{},"+",[591,1148,1129],{},[641,1150,644],{"stretchy":643},[591,1152,593],{},[641,1154,649],{"stretchy":643},[591,1156,639],{},[641,1158,644],{"stretchy":643},[591,1160,593],{},[641,1162,649],{"stretchy":643},[595,1164,1165],{"encoding":597},"-u(x)v(x) + u(x)v(x)",[572,1167,1169,1213],{"className":1168,"ariaHidden":602},[601],[572,1170,1172,1175,1178,1181,1184,1187,1190,1193,1196,1199,1202,1206,1210],{"className":1171},[606],[572,1173],{"className":1174,"style":662},[610],[572,1176,754],{"className":1177},[615],[572,1179,1129],{"className":1180},[615,616],[572,1182,644],{"className":1183},[670],[572,1185,593],{"className":1186},[615,616],[572,1188,649],{"className":1189},[677],[572,1191,639],{"className":1192,"style":666},[615,616],[572,1194,644],{"className":1195},[670],[572,1197,593],{"className":1198},[615,616],[572,1200,649],{"className":1201},[677],[572,1203],{"className":1204,"style":1205},[893],"margin-right:0.2222em;",[572,1207,1146],{"className":1208},[1209],"mbin",[572,1211],{"className":1212,"style":1205},[893],[572,1214,1216,1219,1222,1225,1228,1231,1234,1237,1240],{"className":1215},[606],[572,1217],{"className":1218,"style":662},[610],[572,1220,1129],{"className":1221},[615,616],[572,1223,644],{"className":1224},[670],[572,1226,593],{"className":1227},[615,616],[572,1229,649],{"className":1230},[677],[572,1232,639],{"className":1233,"style":666},[615,616],[572,1235,644],{"className":1236},[670],[572,1238,593],{"className":1239},[615,616],[572,1241,649],{"className":1242},[677],":",[572,1245,1248],{"className":1246},[1247],"katex-display",[572,1249,1251,1434],{"className":1250},[575],[572,1252,1254],{"className":1253},[579],[581,1255,1257],{"xmlns":583,"display":1256},"block",[585,1258,1259,1431],{},[588,1260,1261,1322,1324],{},[727,1262,1263,1320],{},[588,1264,1265,1296,1298],{},[727,1266,1267,1282],{},[588,1268,1269,1271,1273,1275,1277,1280],{},[591,1270,1129],{},[641,1272,644],{"stretchy":643},[591,1274,593],{},[641,1276,1146],{},[591,1278,1279],{},"h",[641,1281,649],{"stretchy":643},[588,1283,1284,1286,1288,1290,1292,1294],{},[591,1285,639],{},[641,1287,644],{"stretchy":643},[591,1289,593],{},[641,1291,1146],{},[591,1293,1279],{},[641,1295,649],{"stretchy":643},[641,1297,754],{},[727,1299,1300,1310],{},[588,1301,1302,1304,1306,1308],{},[591,1303,1129],{},[641,1305,644],{"stretchy":643},[591,1307,593],{},[641,1309,649],{"stretchy":643},[588,1311,1312,1314,1316,1318],{},[591,1313,639],{},[641,1315,644],{"stretchy":643},[591,1317,593],{},[641,1319,649],{"stretchy":643},[591,1321,1279],{},[641,1323,743],{},[727,1325,1326,1407],{},[588,1327,1328,1356,1359,1361,1363,1365,1367,1369,1371,1373,1375,1377,1379],{},[727,1329,1330,1354],{},[588,1331,1332,1334,1336,1338,1340,1342,1344,1346,1348,1350,1352],{},[591,1333,1129],{},[641,1335,644],{"stretchy":643},[591,1337,593],{},[641,1339,1146],{},[591,1341,1279],{},[641,1343,649],{"stretchy":643},[641,1345,754],{},[591,1347,1129],{},[641,1349,644],{"stretchy":643},[591,1351,593],{},[641,1353,649],{"stretchy":643},[591,1355,1279],{},[641,1357,1358],{},"⋅",[591,1360,639],{},[641,1362,644],{"stretchy":643},[591,1364,593],{},[641,1366,649],{"stretchy":643},[641,1368,754],{},[591,1370,1129],{},[641,1372,644],{"stretchy":643},[591,1374,593],{},[641,1376,649],{"stretchy":643},[641,1378,1358],{},[727,1380,1381,1405],{},[588,1382,1383,1385,1387,1389,1391,1393,1395,1397,1399,1401,1403],{},[591,1384,639],{},[641,1386,644],{"stretchy":643},[591,1388,593],{},[641,1390,1146],{},[591,1392,1279],{},[641,1394,649],{"stretchy":643},[641,1396,754],{},[591,1398,639],{},[641,1400,644],{"stretchy":643},[591,1402,593],{},[641,1404,649],{"stretchy":643},[591,1406,1279],{},[588,1408,1409,1411,1413,1415,1417,1419,1421,1423,1425,1427,1429],{},[591,1410,639],{},[641,1412,644],{"stretchy":643},[591,1414,593],{},[641,1416,1146],{},[591,1418,1279],{},[641,1420,649],{"stretchy":643},[641,1422,1358],{},[591,1424,639],{},[641,1426,644],{"stretchy":643},[591,1428,593],{},[641,1430,649],{"stretchy":643},[595,1432,1433],{"encoding":597},"\\frac{\\frac{u(x+h)}{v(x+h)} - \\frac{u(x)}{v(x)}}{h} = \\frac{\\frac{u(x+h) - u(x)}{h} \\cdot v(x) - u(x) \\cdot \\frac{v(x+h) - v(x)}{h}}{v(x+h) \\cdot v(x)}",[572,1435,1437,1714],{"className":1436,"ariaHidden":602},[601],[572,1438,1440,1444,1705,1708,1711],{"className":1439},[606],[572,1441],{"className":1442,"style":1443},[610],"height:2.606em;vertical-align:-0.686em;",[572,1445,1447,1450,1702],{"className":1446},[615],[572,1448],{"className":1449},[670,776],[572,1451,1453],{"className":1452},[727],[572,1454,1456,1693],{"className":1455},[783,784],[572,1457,1459,1690],{"className":1458},[788],[572,1460,1463,1476,1485],{"className":1461,"style":1462},[792],"height:1.92em;",[572,1464,1466,1470],{"style":1465},"top:-2.324em;",[572,1467],{"className":1468,"style":1469},[800],"height:3.01em;",[572,1471,1473],{"className":1472},[615],[572,1474,1279],{"className":1475},[615,616],[572,1477,1479,1482],{"style":1478},"top:-3.24em;",[572,1480],{"className":1481,"style":1469},[800],[572,1483],{"className":1484,"style":857},[856],[572,1486,1488,1491],{"style":1487},"top:-3.92em;",[572,1489],{"className":1490,"style":1469},[800],[572,1492,1494,1595,1598,1601,1604],{"className":1493},[615],[572,1495,1497,1500,1592],{"className":1496},[615],[572,1498],{"className":1499},[670,776],[572,1501,1503],{"className":1502},[727],[572,1504,1506,1583],{"className":1505},[783,784],[572,1507,1509,1580],{"className":1508},[788],[572,1510,1513,1542,1550],{"className":1511,"style":1512},[792],"height:1.01em;",[572,1514,1515,1518],{"style":796},[572,1516],{"className":1517,"style":801},[800],[572,1519,1521],{"className":1520},[805,806,807,808],[572,1522,1524,1527,1530,1533,1536,1539],{"className":1523},[615,808],[572,1525,639],{"className":1526,"style":666},[615,616,808],[572,1528,644],{"className":1529},[670,808],[572,1531,593],{"className":1532},[615,616,808],[572,1534,1146],{"className":1535},[1209,808],[572,1537,1279],{"className":1538},[615,616,808],[572,1540,649],{"className":1541},[677,808],[572,1543,1544,1547],{"style":849},[572,1545],{"className":1546,"style":801},[800],[572,1548],{"className":1549,"style":857},[856],[572,1551,1553,1556],{"style":1552},"top:-3.485em;",[572,1554],{"className":1555,"style":801},[800],[572,1557,1559],{"className":1558},[805,806,807,808],[572,1560,1562,1565,1568,1571,1574,1577],{"className":1561},[615,808],[572,1563,1129],{"className":1564},[615,616,808],[572,1566,644],{"className":1567},[670,808],[572,1569,593],{"className":1570},[615,616,808],[572,1572,1146],{"className":1573},[1209,808],[572,1575,1279],{"className":1576},[615,616,808],[572,1578,649],{"className":1579},[677,808],[572,1581,877],{"className":1582},[876],[572,1584,1586],{"className":1585},[788],[572,1587,1590],{"className":1588,"style":1589},[792],"height:0.52em;",[572,1591],{},[572,1593],{"className":1594},[677,776],[572,1596],{"className":1597,"style":1205},[893],[572,1599,754],{"className":1600},[1209],[572,1602],{"className":1603,"style":1205},[893],[572,1605,1607,1610,1687],{"className":1606},[615],[572,1608],{"className":1609},[670,776],[572,1611,1613],{"className":1612},[727],[572,1614,1616,1679],{"className":1615},[783,784],[572,1617,1619,1676],{"className":1618},[788],[572,1620,1622,1645,1653],{"className":1621,"style":1512},[792],[572,1623,1624,1627],{"style":796},[572,1625],{"className":1626,"style":801},[800],[572,1628,1630],{"className":1629},[805,806,807,808],[572,1631,1633,1636,1639,1642],{"className":1632},[615,808],[572,1634,639],{"className":1635,"style":666},[615,616,808],[572,1637,644],{"className":1638},[670,808],[572,1640,593],{"className":1641},[615,616,808],[572,1643,649],{"className":1644},[677,808],[572,1646,1647,1650],{"style":849},[572,1648],{"className":1649,"style":801},[800],[572,1651],{"className":1652,"style":857},[856],[572,1654,1655,1658],{"style":1552},[572,1656],{"className":1657,"style":801},[800],[572,1659,1661],{"className":1660},[805,806,807,808],[572,1662,1664,1667,1670,1673],{"className":1663},[615,808],[572,1665,1129],{"className":1666},[615,616,808],[572,1668,644],{"className":1669},[670,808],[572,1671,593],{"className":1672},[615,616,808],[572,1674,649],{"className":1675},[677,808],[572,1677,877],{"className":1678},[876],[572,1680,1682],{"className":1681},[788],[572,1683,1685],{"className":1684,"style":1589},[792],[572,1686],{},[572,1688],{"className":1689},[677,776],[572,1691,877],{"className":1692},[876],[572,1694,1696],{"className":1695},[788],[572,1697,1700],{"className":1698,"style":1699},[792],"height:0.686em;",[572,1701],{},[572,1703],{"className":1704},[677,776],[572,1706],{"className":1707,"style":894},[893],[572,1709,743],{"className":1710},[898],[572,1712],{"className":1713,"style":894},[893],[572,1715,1717,1721],{"className":1716},[606],[572,1718],{"className":1719,"style":1720},[610],"height:2.681em;vertical-align:-0.936em;",[572,1722,1724,1727,2069],{"className":1723},[615],[572,1725],{"className":1726},[670,776],[572,1728,1730],{"className":1729},[727],[572,1731,1733,2060],{"className":1732},[783,784],[572,1734,1736,2057],{"className":1735},[788],[572,1737,1740,1793,1801],{"className":1738,"style":1739},[792],"height:1.745em;",[572,1741,1742,1745],{"style":1465},[572,1743],{"className":1744,"style":1469},[800],[572,1746,1748,1751,1754,1757,1760,1763,1766,1769,1772,1775,1778,1781,1784,1787,1790],{"className":1747},[615],[572,1749,639],{"className":1750,"style":666},[615,616],[572,1752,644],{"className":1753},[670],[572,1755,593],{"className":1756},[615,616],[572,1758],{"className":1759,"style":1205},[893],[572,1761,1146],{"className":1762},[1209],[572,1764],{"className":1765,"style":1205},[893],[572,1767,1279],{"className":1768},[615,616],[572,1770,649],{"className":1771},[677],[572,1773],{"className":1774,"style":1205},[893],[572,1776,1358],{"className":1777},[1209],[572,1779],{"className":1780,"style":1205},[893],[572,1782,639],{"className":1783,"style":666},[615,616],[572,1785,644],{"className":1786},[670],[572,1788,593],{"className":1789},[615,616],[572,1791,649],{"className":1792},[677],[572,1794,1795,1798],{"style":1478},[572,1796],{"className":1797,"style":1469},[800],[572,1799],{"className":1800,"style":857},[856],[572,1802,1804,1807],{"style":1803},"top:-3.745em;",[572,1805],{"className":1806,"style":1469},[800],[572,1808,1810,1908,1911,1914,1917,1920,1923,1926,1929,1932,1935,1938,1941,1944,1947,1950,1953,1956,1959],{"className":1809},[615],[572,1811,1813,1816,1905],{"className":1812},[615],[572,1814],{"className":1815},[670,776],[572,1817,1819],{"className":1818},[727],[572,1820,1822,1897],{"className":1821},[783,784],[572,1823,1825,1894],{"className":1824},[788],[572,1826,1828,1842,1850],{"className":1827,"style":1512},[792],[572,1829,1830,1833],{"style":796},[572,1831],{"className":1832,"style":801},[800],[572,1834,1836],{"className":1835},[805,806,807,808],[572,1837,1839],{"className":1838},[615,808],[572,1840,1279],{"className":1841},[615,616,808],[572,1843,1844,1847],{"style":849},[572,1845],{"className":1846,"style":801},[800],[572,1848],{"className":1849,"style":857},[856],[572,1851,1852,1855],{"style":1552},[572,1853],{"className":1854,"style":801},[800],[572,1856,1858],{"className":1857},[805,806,807,808],[572,1859,1861,1864,1867,1870,1873,1876,1879,1882,1885,1888,1891],{"className":1860},[615,808],[572,1862,1129],{"className":1863},[615,616,808],[572,1865,644],{"className":1866},[670,808],[572,1868,593],{"className":1869},[615,616,808],[572,1871,1146],{"className":1872},[1209,808],[572,1874,1279],{"className":1875},[615,616,808],[572,1877,649],{"className":1878},[677,808],[572,1880,754],{"className":1881},[1209,808],[572,1883,1129],{"className":1884},[615,616,808],[572,1886,644],{"className":1887},[670,808],[572,1889,593],{"className":1890},[615,616,808],[572,1892,649],{"className":1893},[677,808],[572,1895,877],{"className":1896},[876],[572,1898,1900],{"className":1899},[788],[572,1901,1903],{"className":1902,"style":884},[792],[572,1904],{},[572,1906],{"className":1907},[677,776],[572,1909],{"className":1910,"style":1205},[893],[572,1912,1358],{"className":1913},[1209],[572,1915],{"className":1916,"style":1205},[893],[572,1918,639],{"className":1919,"style":666},[615,616],[572,1921,644],{"className":1922},[670],[572,1924,593],{"className":1925},[615,616],[572,1927,649],{"className":1928},[677],[572,1930],{"className":1931,"style":1205},[893],[572,1933,754],{"className":1934},[1209],[572,1936],{"className":1937,"style":1205},[893],[572,1939,1129],{"className":1940},[615,616],[572,1942,644],{"className":1943},[670],[572,1945,593],{"className":1946},[615,616],[572,1948,649],{"className":1949},[677],[572,1951],{"className":1952,"style":1205},[893],[572,1954,1358],{"className":1955},[1209],[572,1957],{"className":1958,"style":1205},[893],[572,1960,1962,1965,2054],{"className":1961},[615],[572,1963],{"className":1964},[670,776],[572,1966,1968],{"className":1967},[727],[572,1969,1971,2046],{"className":1970},[783,784],[572,1972,1974,2043],{"className":1973},[788],[572,1975,1977,1991,1999],{"className":1976,"style":1512},[792],[572,1978,1979,1982],{"style":796},[572,1980],{"className":1981,"style":801},[800],[572,1983,1985],{"className":1984},[805,806,807,808],[572,1986,1988],{"className":1987},[615,808],[572,1989,1279],{"className":1990},[615,616,808],[572,1992,1993,1996],{"style":849},[572,1994],{"className":1995,"style":801},[800],[572,1997],{"className":1998,"style":857},[856],[572,2000,2001,2004],{"style":1552},[572,2002],{"className":2003,"style":801},[800],[572,2005,2007],{"className":2006},[805,806,807,808],[572,2008,2010,2013,2016,2019,2022,2025,2028,2031,2034,2037,2040],{"className":2009},[615,808],[572,2011,639],{"className":2012,"style":666},[615,616,808],[572,2014,644],{"className":2015},[670,808],[572,2017,593],{"className":2018},[615,616,808],[572,2020,1146],{"className":2021},[1209,808],[572,2023,1279],{"className":2024},[615,616,808],[572,2026,649],{"className":2027},[677,808],[572,2029,754],{"className":2030},[1209,808],[572,2032,639],{"className":2033,"style":666},[615,616,808],[572,2035,644],{"className":2036},[670,808],[572,2038,593],{"className":2039},[615,616,808],[572,2041,649],{"className":2042},[677,808],[572,2044,877],{"className":2045},[876],[572,2047,2049],{"className":2048},[788],[572,2050,2052],{"className":2051,"style":884},[792],[572,2053],{},[572,2055],{"className":2056},[677,776],[572,2058,877],{"className":2059},[876],[572,2061,2063],{"className":2062},[788],[572,2064,2067],{"className":2065,"style":2066},[792],"height:0.936em;",[572,2068],{},[572,2070],{"className":2071},[677,776],[564,2073,2074,2075,2130],{},"Für ",[572,2076,2078,2098],{"className":2077},[575],[572,2079,2081],{"className":2080},[579],[581,2082,2083],{"xmlns":583},[585,2084,2085,2095],{},[588,2086,2087,2089,2092],{},[591,2088,1279],{},[641,2090,2091],{},"→",[730,2093,2094],{},"0",[595,2096,2097],{"encoding":597},"h \\to 0",[572,2099,2101,2120],{"className":2100,"ariaHidden":602},[601],[572,2102,2104,2108,2111,2114,2117],{"className":2103},[606],[572,2105],{"className":2106,"style":2107},[610],"height:0.6944em;",[572,2109,1279],{"className":2110},[615,616],[572,2112],{"className":2113,"style":894},[893],[572,2115,2091],{"className":2116},[898],[572,2118],{"className":2119,"style":894},[893],[572,2121,2123,2127],{"className":2122},[606],[572,2124],{"className":2125,"style":2126},[610],"height:0.6444em;",[572,2128,2094],{"className":2129},[615]," ergibt sich die Quotientenregel.",[559,2132,2134],{"id":2133},"beispiele","Beispiele",[564,2136,2137,2304,2305,2397,2398,2477,2478,2477,2562,2477,2636,1243],{},[572,2138,2140,2183],{"className":2139},[575],[572,2141,2143],{"className":2142},[579],[581,2144,2145],{"xmlns":583},[585,2146,2147,2180],{},[588,2148,2149,2151,2153,2155,2157,2159],{},[591,2150,693],{},[641,2152,644],{"stretchy":643},[591,2154,593],{},[641,2156,649],{"stretchy":643},[641,2158,743],{},[727,2160,2161,2172],{},[588,2162,2163,2165,2167,2169],{},[730,2164,740],{},[591,2166,593],{},[641,2168,1146],{},[730,2170,2171],{},"1",[588,2173,2174,2176,2178],{},[591,2175,593],{},[641,2177,754],{},[730,2179,732],{},[595,2181,2182],{"encoding":597},"f(x) = \\frac{2x + 1}{x - 3}",[572,2184,2186,2213],{"className":2185,"ariaHidden":602},[601],[572,2187,2189,2192,2195,2198,2201,2204,2207,2210],{"className":2188},[606],[572,2190],{"className":2191,"style":662},[610],[572,2193,693],{"className":2194,"style":709},[615,616],[572,2196,644],{"className":2197},[670],[572,2199,593],{"className":2200},[615,616],[572,2202,649],{"className":2203},[677],[572,2205],{"className":2206,"style":894},[893],[572,2208,743],{"className":2209},[898],[572,2211],{"className":2212,"style":894},[893],[572,2214,2216,2220],{"className":2215},[606],[572,2217],{"className":2218,"style":2219},[610],"height:1.2484em;vertical-align:-0.4033em;",[572,2221,2223,2226,2301],{"className":2222},[615],[572,2224],{"className":2225},[670,776],[572,2227,2229],{"className":2228},[727],[572,2230,2232,2292],{"className":2231},[783,784],[572,2233,2235,2289],{"className":2234},[788],[572,2236,2238,2258,2266],{"className":2237,"style":793},[792],[572,2239,2240,2243],{"style":796},[572,2241],{"className":2242,"style":801},[800],[572,2244,2246],{"className":2245},[805,806,807,808],[572,2247,2249,2252,2255],{"className":2248},[615,808],[572,2250,593],{"className":2251},[615,616,808],[572,2253,754],{"className":2254},[1209,808],[572,2256,732],{"className":2257},[615,808],[572,2259,2260,2263],{"style":849},[572,2261],{"className":2262,"style":801},[800],[572,2264],{"className":2265,"style":857},[856],[572,2267,2268,2271],{"style":860},[572,2269],{"className":2270,"style":801},[800],[572,2272,2274],{"className":2273},[805,806,807,808],[572,2275,2277,2280,2283,2286],{"className":2276},[615,808],[572,2278,740],{"className":2279},[615,808],[572,2281,593],{"className":2282},[615,616,808],[572,2284,1146],{"className":2285},[1209,808],[572,2287,2171],{"className":2288},[615,808],[572,2290,877],{"className":2291},[876],[572,2293,2295],{"className":2294},[788],[572,2296,2299],{"className":2297,"style":2298},[792],"height:0.4033em;",[572,2300],{},[572,2302],{"className":2303},[677,776]," für ",[572,2306,2308,2327],{"className":2307},[575],[572,2309,2311],{"className":2310},[579],[581,2312,2313],{"xmlns":583},[585,2314,2315,2324],{},[588,2316,2317,2319,2322],{},[591,2318,593],{},[641,2320,2321],{"mathvariant":968},"≠",[730,2323,732],{},[595,2325,2326],{"encoding":597},"x \\neq 3",[572,2328,2330,2388],{"className":2329,"ariaHidden":602},[601],[572,2331,2333,2336,2339,2342,2385],{"className":2332},[606],[572,2334],{"className":2335,"style":705},[610],[572,2337,593],{"className":2338},[615,616],[572,2340],{"className":2341,"style":894},[893],[572,2343,2345,2378,2382],{"className":2344},[898],[572,2346,2348],{"className":2347},[898],[572,2349,2352],{"className":2350},[615,2351],"vbox",[572,2353,2356],{"className":2354},[2355],"thinbox",[572,2357,2360,2363,2374],{"className":2358},[2359],"rlap",[572,2361],{"className":2362,"style":705},[610],[572,2364,2367],{"className":2365},[2366],"inner",[572,2368,2370],{"className":2369},[615],[572,2371,2373],{"className":2372},[898],"",[572,2375],{"className":2376},[2377],"fix",[572,2379],{"className":2380},[893,2381],"nobreak",[572,2383,743],{"className":2384},[898],[572,2386],{"className":2387,"style":894},[893],[572,2389,2391,2394],{"className":2390},[606],[572,2392],{"className":2393,"style":2126},[610],[572,2395,732],{"className":2396},[615],", mit ",[572,2399,2401,2425],{"className":2400},[575],[572,2402,2404],{"className":2403},[579],[581,2405,2406],{"xmlns":583},[585,2407,2408,2422],{},[588,2409,2410,2412,2414,2416,2418,2420],{},[591,2411,1129],{},[641,2413,743],{},[730,2415,740],{},[591,2417,593],{},[641,2419,1146],{},[730,2421,2171],{},[595,2423,2424],{"encoding":597},"u = 2x + 1",[572,2426,2428,2446,2468],{"className":2427,"ariaHidden":602},[601],[572,2429,2431,2434,2437,2440,2443],{"className":2430},[606],[572,2432],{"className":2433,"style":611},[610],[572,2435,1129],{"className":2436},[615,616],[572,2438],{"className":2439,"style":894},[893],[572,2441,743],{"className":2442},[898],[572,2444],{"className":2445,"style":894},[893],[572,2447,2449,2453,2456,2459,2462,2465],{"className":2448},[606],[572,2450],{"className":2451,"style":2452},[610],"height:0.7278em;vertical-align:-0.0833em;",[572,2454,740],{"className":2455},[615],[572,2457,593],{"className":2458},[615,616],[572,2460],{"className":2461,"style":1205},[893],[572,2463,1146],{"className":2464},[1209],[572,2466],{"className":2467,"style":1205},[893],[572,2469,2471,2474],{"className":2470},[606],[572,2472],{"className":2473,"style":2126},[610],[572,2475,2171],{"className":2476},[615],", ",[572,2479,2481,2503],{"className":2480},[575],[572,2482,2484],{"className":2483},[579],[581,2485,2486],{"xmlns":583},[585,2487,2488,2500],{},[588,2489,2490,2496,2498],{},[734,2491,2492,2494],{},[591,2493,1129],{},[641,2495,970],{"mathvariant":968,"lspace":969,"rspace":969},[641,2497,743],{},[730,2499,740],{},[595,2501,2502],{"encoding":597},"u' = 2",[572,2504,2506,2553],{"className":2505,"ariaHidden":602},[601],[572,2507,2509,2512,2544,2547,2550],{"className":2508},[606],[572,2510],{"className":2511,"style":1025},[610],[572,2513,2515,2518],{"className":2514},[615],[572,2516,1129],{"className":2517},[615,616],[572,2519,2521],{"className":2520},[821],[572,2522,2524],{"className":2523},[783],[572,2525,2527],{"className":2526},[788],[572,2528,2530],{"className":2529,"style":1025},[792],[572,2531,2532,2535],{"style":932},[572,2533],{"className":2534,"style":936},[800],[572,2536,2538],{"className":2537},[805,806,807,808],[572,2539,2541],{"className":2540},[615,808],[572,2542,970],{"className":2543},[615,808],[572,2545],{"className":2546,"style":894},[893],[572,2548,743],{"className":2549},[898],[572,2551],{"className":2552,"style":894},[893],[572,2554,2556,2559],{"className":2555},[606],[572,2557],{"className":2558,"style":2126},[610],[572,2560,740],{"className":2561},[615],[572,2563,2565,2587],{"className":2564},[575],[572,2566,2568],{"className":2567},[579],[581,2569,2570],{"xmlns":583},[585,2571,2572,2584],{},[588,2573,2574,2576,2578,2580,2582],{},[591,2575,639],{},[641,2577,743],{},[591,2579,593],{},[641,2581,754],{},[730,2583,732],{},[595,2585,2586],{"encoding":597},"v = x - 3",[572,2588,2590,2608,2627],{"className":2589,"ariaHidden":602},[601],[572,2591,2593,2596,2599,2602,2605],{"className":2592},[606],[572,2594],{"className":2595,"style":611},[610],[572,2597,639],{"className":2598,"style":666},[615,616],[572,2600],{"className":2601,"style":894},[893],[572,2603,743],{"className":2604},[898],[572,2606],{"className":2607,"style":894},[893],[572,2609,2611,2615,2618,2621,2624],{"className":2610},[606],[572,2612],{"className":2613,"style":2614},[610],"height:0.6667em;vertical-align:-0.0833em;",[572,2616,593],{"className":2617},[615,616],[572,2619],{"className":2620,"style":1205},[893],[572,2622,754],{"className":2623},[1209],[572,2625],{"className":2626,"style":1205},[893],[572,2628,2630,2633],{"className":2629},[606],[572,2631],{"className":2632,"style":2126},[610],[572,2634,732],{"className":2635},[615],[572,2637,2639,2661],{"className":2638},[575],[572,2640,2642],{"className":2641},[579],[581,2643,2644],{"xmlns":583},[585,2645,2646,2658],{},[588,2647,2648,2654,2656],{},[734,2649,2650,2652],{},[591,2651,639],{},[641,2653,970],{"mathvariant":968,"lspace":969,"rspace":969},[641,2655,743],{},[730,2657,2171],{},[595,2659,2660],{"encoding":597},"v' = 1",[572,2662,2664,2711],{"className":2663,"ariaHidden":602},[601],[572,2665,2667,2670,2702,2705,2708],{"className":2666},[606],[572,2668],{"className":2669,"style":1025},[610],[572,2671,2673,2676],{"className":2672},[615],[572,2674,639],{"className":2675,"style":666},[615,616],[572,2677,2679],{"className":2678},[821],[572,2680,2682],{"className":2681},[783],[572,2683,2685],{"className":2684},[788],[572,2686,2688],{"className":2687,"style":1025},[792],[572,2689,2690,2693],{"style":932},[572,2691],{"className":2692,"style":936},[800],[572,2694,2696],{"className":2695},[805,806,807,808],[572,2697,2699],{"className":2698},[615,808],[572,2700,970],{"className":2701},[615,808],[572,2703],{"className":2704,"style":894},[893],[572,2706,743],{"className":2707},[898],[572,2709],{"className":2710,"style":894},[893],[572,2712,2714,2717],{"className":2713},[606],[572,2715],{"className":2716,"style":2126},[610],[572,2718,2171],{"className":2719},[615],[572,2721,2723],{"className":2722},[1247],[572,2724,2726,2831],{"className":2725},[575],[572,2727,2729],{"className":2728},[579],[581,2730,2731],{"xmlns":583,"display":1256},[585,2732,2733,2828],{},[588,2734,2735,2741,2743,2745,2747,2749,2801,2803],{},[734,2736,2737,2739],{},[591,2738,693],{},[641,2740,970],{"mathvariant":968,"lspace":969,"rspace":969},[641,2742,644],{"stretchy":643},[591,2744,593],{},[641,2746,649],{"stretchy":643},[641,2748,743],{},[727,2750,2751,2785],{},[588,2752,2753,2755,2757,2759,2761,2763,2765,2767,2769,2771,2773,2775,2777,2779,2781,2783],{},[730,2754,740],{},[641,2756,1358],{},[641,2758,644],{"stretchy":643},[591,2760,593],{},[641,2762,754],{},[730,2764,732],{},[641,2766,649],{"stretchy":643},[641,2768,754],{},[641,2770,644],{"stretchy":643},[730,2772,740],{},[591,2774,593],{},[641,2776,1146],{},[730,2778,2171],{},[641,2780,649],{"stretchy":643},[641,2782,1358],{},[730,2784,2171],{},[588,2786,2787,2789,2791,2793,2795],{},[641,2788,644],{"stretchy":643},[591,2790,593],{},[641,2792,754],{},[730,2794,732],{},[734,2796,2797,2799],{},[641,2798,649],{"stretchy":643},[730,2800,740],{},[641,2802,743],{},[727,2804,2805,2812],{},[588,2806,2807,2809],{},[641,2808,754],{},[730,2810,2811],{},"7",[588,2813,2814,2816,2818,2820,2822],{},[641,2815,644],{"stretchy":643},[591,2817,593],{},[641,2819,754],{},[730,2821,732],{},[734,2823,2824,2826],{},[641,2825,649],{"stretchy":643},[730,2827,740],{},[595,2829,2830],{"encoding":597},"f'(x) = \\frac{2 \\cdot (x - 3) - (2x + 1) \\cdot 1}{(x - 3)^2} = \\frac{-7}{(x - 3)^2}",[572,2832,2834,2893,3095],{"className":2833,"ariaHidden":602},[601],[572,2835,2837,2841,2875,2878,2881,2884,2887,2890],{"className":2836},[606],[572,2838],{"className":2839,"style":2840},[610],"height:1.0519em;vertical-align:-0.25em;",[572,2842,2844,2847],{"className":2843},[615],[572,2845,693],{"className":2846,"style":709},[615,616],[572,2848,2850],{"className":2849},[821],[572,2851,2853],{"className":2852},[783],[572,2854,2856],{"className":2855},[788],[572,2857,2860],{"className":2858,"style":2859},[792],"height:0.8019em;",[572,2861,2863,2866],{"style":2862},"top:-3.113em;margin-right:0.05em;",[572,2864],{"className":2865,"style":936},[800],[572,2867,2869],{"className":2868},[805,806,807,808],[572,2870,2872],{"className":2871},[615,808],[572,2873,970],{"className":2874},[615,808],[572,2876,644],{"className":2877},[670],[572,2879,593],{"className":2880},[615,616],[572,2882,649],{"className":2883},[677],[572,2885],{"className":2886,"style":894},[893],[572,2888,743],{"className":2889},[898],[572,2891],{"className":2892,"style":894},[893],[572,2894,2896,2900,3086,3089,3092],{"className":2895},[606],[572,2897],{"className":2898,"style":2899},[610],"height:2.363em;vertical-align:-0.936em;",[572,2901,2903,2906,3083],{"className":2902},[615],[572,2904],{"className":2905},[670,776],[572,2907,2909],{"className":2908},[727],[572,2910,2912,3075],{"className":2911},[783,784],[572,2913,2915,3072],{"className":2914},[788],[572,2916,2919,2977,2985],{"className":2917,"style":2918},[792],"height:1.427em;",[572,2920,2922,2925],{"style":2921},"top:-2.314em;",[572,2923],{"className":2924,"style":801},[800],[572,2926,2928,2931,2934,2937,2940,2943,2946],{"className":2927},[615],[572,2929,644],{"className":2930},[670],[572,2932,593],{"className":2933},[615,616],[572,2935],{"className":2936,"style":1205},[893],[572,2938,754],{"className":2939},[1209],[572,2941],{"className":2942,"style":1205},[893],[572,2944,732],{"className":2945},[615],[572,2947,2949,2952],{"className":2948},[677],[572,2950,649],{"className":2951},[677],[572,2953,2955],{"className":2954},[821],[572,2956,2958],{"className":2957},[783],[572,2959,2961],{"className":2960},[788],[572,2962,2965],{"className":2963,"style":2964},[792],"height:0.7401em;",[572,2966,2968,2971],{"style":2967},"top:-2.989em;margin-right:0.05em;",[572,2969],{"className":2970,"style":936},[800],[572,2972,2974],{"className":2973},[805,806,807,808],[572,2975,740],{"className":2976},[615,808],[572,2978,2979,2982],{"style":849},[572,2980],{"className":2981,"style":801},[800],[572,2983],{"className":2984,"style":857},[856],[572,2986,2988,2991],{"style":2987},"top:-3.677em;",[572,2989],{"className":2990,"style":801},[800],[572,2992,2994,2997,3000,3003,3006,3009,3012,3015,3018,3021,3024,3027,3030,3033,3036,3039,3042,3045,3048,3051,3054,3057,3060,3063,3066,3069],{"className":2993},[615],[572,2995,740],{"className":2996},[615],[572,2998],{"className":2999,"style":1205},[893],[572,3001,1358],{"className":3002},[1209],[572,3004],{"className":3005,"style":1205},[893],[572,3007,644],{"className":3008},[670],[572,3010,593],{"className":3011},[615,616],[572,3013],{"className":3014,"style":1205},[893],[572,3016,754],{"className":3017},[1209],[572,3019],{"className":3020,"style":1205},[893],[572,3022,732],{"className":3023},[615],[572,3025,649],{"className":3026},[677],[572,3028],{"className":3029,"style":1205},[893],[572,3031,754],{"className":3032},[1209],[572,3034],{"className":3035,"style":1205},[893],[572,3037,644],{"className":3038},[670],[572,3040,740],{"className":3041},[615],[572,3043,593],{"className":3044},[615,616],[572,3046],{"className":3047,"style":1205},[893],[572,3049,1146],{"className":3050},[1209],[572,3052],{"className":3053,"style":1205},[893],[572,3055,2171],{"className":3056},[615],[572,3058,649],{"className":3059},[677],[572,3061],{"className":3062,"style":1205},[893],[572,3064,1358],{"className":3065},[1209],[572,3067],{"className":3068,"style":1205},[893],[572,3070,2171],{"className":3071},[615],[572,3073,877],{"className":3074},[876],[572,3076,3078],{"className":3077},[788],[572,3079,3081],{"className":3080,"style":2066},[792],[572,3082],{},[572,3084],{"className":3085},[677,776],[572,3087],{"className":3088,"style":894},[893],[572,3090,743],{"className":3091},[898],[572,3093],{"className":3094,"style":894},[893],[572,3096,3098,3102],{"className":3097},[606],[572,3099],{"className":3100,"style":3101},[610],"height:2.2574em;vertical-align:-0.936em;",[572,3103,3105,3108,3209],{"className":3104},[615],[572,3106],{"className":3107},[670,776],[572,3109,3111],{"className":3110},[727],[572,3112,3114,3201],{"className":3113},[783,784],[572,3115,3117,3198],{"className":3116},[788],[572,3118,3121,3176,3184],{"className":3119,"style":3120},[792],"height:1.3214em;",[572,3122,3123,3126],{"style":2921},[572,3124],{"className":3125,"style":801},[800],[572,3127,3129,3132,3135,3138,3141,3144,3147],{"className":3128},[615],[572,3130,644],{"className":3131},[670],[572,3133,593],{"className":3134},[615,616],[572,3136],{"className":3137,"style":1205},[893],[572,3139,754],{"className":3140},[1209],[572,3142],{"className":3143,"style":1205},[893],[572,3145,732],{"className":3146},[615],[572,3148,3150,3153],{"className":3149},[677],[572,3151,649],{"className":3152},[677],[572,3154,3156],{"className":3155},[821],[572,3157,3159],{"className":3158},[783],[572,3160,3162],{"className":3161},[788],[572,3163,3165],{"className":3164,"style":2964},[792],[572,3166,3167,3170],{"style":2967},[572,3168],{"className":3169,"style":936},[800],[572,3171,3173],{"className":3172},[805,806,807,808],[572,3174,740],{"className":3175},[615,808],[572,3177,3178,3181],{"style":849},[572,3179],{"className":3180,"style":801},[800],[572,3182],{"className":3183,"style":857},[856],[572,3185,3186,3189],{"style":2987},[572,3187],{"className":3188,"style":801},[800],[572,3190,3192,3195],{"className":3191},[615],[572,3193,754],{"className":3194},[615],[572,3196,2811],{"className":3197},[615],[572,3199,877],{"className":3200},[876],[572,3202,3204],{"className":3203},[788],[572,3205,3207],{"className":3206,"style":2066},[792],[572,3208],{},[572,3210],{"className":3211},[677,776],[564,3213,3214,3393,3394,2477,3445,2477,3529,2477,3632,1243],{},[572,3215,3217,3255],{"className":3216},[575],[572,3218,3220],{"className":3219},[579],[581,3221,3222],{"xmlns":583},[585,3223,3224,3252],{},[588,3225,3226,3228,3230,3232,3234,3236],{},[591,3227,693],{},[641,3229,644],{"stretchy":643},[591,3231,593],{},[641,3233,649],{"stretchy":643},[641,3235,743],{},[727,3237,3238,3240],{},[591,3239,593],{},[588,3241,3242,3248,3250],{},[734,3243,3244,3246],{},[591,3245,593],{},[730,3247,740],{},[641,3249,1146],{},[730,3251,2171],{},[595,3253,3254],{"encoding":597},"f(x) = \\frac{x}{x^2 + 1}",[572,3256,3258,3285],{"className":3257,"ariaHidden":602},[601],[572,3259,3261,3264,3267,3270,3273,3276,3279,3282],{"className":3260},[606],[572,3262],{"className":3263,"style":662},[610],[572,3265,693],{"className":3266,"style":709},[615,616],[572,3268,644],{"className":3269},[670],[572,3271,593],{"className":3272},[615,616],[572,3274,649],{"className":3275},[677],[572,3277],{"className":3278,"style":894},[893],[572,3280,743],{"className":3281},[898],[572,3283],{"className":3284,"style":894},[893],[572,3286,3288,3292],{"className":3287},[606],[572,3289],{"className":3290,"style":3291},[610],"height:1.0987em;vertical-align:-0.4033em;",[572,3293,3295,3298,3390],{"className":3294},[615],[572,3296],{"className":3297},[670,776],[572,3299,3301],{"className":3300},[727],[572,3302,3304,3382],{"className":3303},[783,784],[572,3305,3307,3379],{"className":3306},[788],[572,3308,3311,3357,3365],{"className":3309,"style":3310},[792],"height:0.6954em;",[572,3312,3313,3316],{"style":796},[572,3314],{"className":3315,"style":801},[800],[572,3317,3319],{"className":3318},[805,806,807,808],[572,3320,3322,3351,3354],{"className":3321},[615,808],[572,3323,3325,3328],{"className":3324},[615,808],[572,3326,593],{"className":3327},[615,616,808],[572,3329,3331],{"className":3330},[821],[572,3332,3334],{"className":3333},[783],[572,3335,3337],{"className":3336},[788],[572,3338,3340],{"className":3339,"style":831},[792],[572,3341,3342,3345],{"style":834},[572,3343],{"className":3344,"style":838},[800],[572,3346,3348],{"className":3347},[805,842,843,808],[572,3349,740],{"className":3350},[615,808],[572,3352,1146],{"className":3353},[1209,808],[572,3355,2171],{"className":3356},[615,808],[572,3358,3359,3362],{"style":849},[572,3360],{"className":3361,"style":801},[800],[572,3363],{"className":3364,"style":857},[856],[572,3366,3367,3370],{"style":860},[572,3368],{"className":3369,"style":801},[800],[572,3371,3373],{"className":3372},[805,806,807,808],[572,3374,3376],{"className":3375},[615,808],[572,3377,593],{"className":3378},[615,616,808],[572,3380,877],{"className":3381},[876],[572,3383,3385],{"className":3384},[788],[572,3386,3388],{"className":3387,"style":2298},[792],[572,3389],{},[572,3391],{"className":3392},[677,776]," mit ",[572,3395,3397,3415],{"className":3396},[575],[572,3398,3400],{"className":3399},[579],[581,3401,3402],{"xmlns":583},[585,3403,3404,3412],{},[588,3405,3406,3408,3410],{},[591,3407,1129],{},[641,3409,743],{},[591,3411,593],{},[595,3413,3414],{"encoding":597},"u = x",[572,3416,3418,3436],{"className":3417,"ariaHidden":602},[601],[572,3419,3421,3424,3427,3430,3433],{"className":3420},[606],[572,3422],{"className":3423,"style":611},[610],[572,3425,1129],{"className":3426},[615,616],[572,3428],{"className":3429,"style":894},[893],[572,3431,743],{"className":3432},[898],[572,3434],{"className":3435,"style":894},[893],[572,3437,3439,3442],{"className":3438},[606],[572,3440],{"className":3441,"style":611},[610],[572,3443,593],{"className":3444},[615,616],[572,3446,3448,3470],{"className":3447},[575],[572,3449,3451],{"className":3450},[579],[581,3452,3453],{"xmlns":583},[585,3454,3455,3467],{},[588,3456,3457,3463,3465],{},[734,3458,3459,3461],{},[591,3460,1129],{},[641,3462,970],{"mathvariant":968,"lspace":969,"rspace":969},[641,3464,743],{},[730,3466,2171],{},[595,3468,3469],{"encoding":597},"u' = 1",[572,3471,3473,3520],{"className":3472,"ariaHidden":602},[601],[572,3474,3476,3479,3511,3514,3517],{"className":3475},[606],[572,3477],{"className":3478,"style":1025},[610],[572,3480,3482,3485],{"className":3481},[615],[572,3483,1129],{"className":3484},[615,616],[572,3486,3488],{"className":3487},[821],[572,3489,3491],{"className":3490},[783],[572,3492,3494],{"className":3493},[788],[572,3495,3497],{"className":3496,"style":1025},[792],[572,3498,3499,3502],{"style":932},[572,3500],{"className":3501,"style":936},[800],[572,3503,3505],{"className":3504},[805,806,807,808],[572,3506,3508],{"className":3507},[615,808],[572,3509,970],{"className":3510},[615,808],[572,3512],{"className":3513,"style":894},[893],[572,3515,743],{"className":3516},[898],[572,3518],{"className":3519,"style":894},[893],[572,3521,3523,3526],{"className":3522},[606],[572,3524],{"className":3525,"style":2126},[610],[572,3527,2171],{"className":3528},[615],[572,3530,3532,3558],{"className":3531},[575],[572,3533,3535],{"className":3534},[579],[581,3536,3537],{"xmlns":583},[585,3538,3539,3555],{},[588,3540,3541,3543,3545,3551,3553],{},[591,3542,639],{},[641,3544,743],{},[734,3546,3547,3549],{},[591,3548,593],{},[730,3550,740],{},[641,3552,1146],{},[730,3554,2171],{},[595,3556,3557],{"encoding":597},"v = x^2 + 1",[572,3559,3561,3579,3623],{"className":3560,"ariaHidden":602},[601],[572,3562,3564,3567,3570,3573,3576],{"className":3563},[606],[572,3565],{"className":3566,"style":611},[610],[572,3568,639],{"className":3569,"style":666},[615,616],[572,3571],{"className":3572,"style":894},[893],[572,3574,743],{"className":3575},[898],[572,3577],{"className":3578,"style":894},[893],[572,3580,3582,3585,3614,3617,3620],{"className":3581},[606],[572,3583],{"className":3584,"style":1064},[610],[572,3586,3588,3591],{"className":3587},[615],[572,3589,593],{"className":3590},[615,616],[572,3592,3594],{"className":3593},[821],[572,3595,3597],{"className":3596},[783],[572,3598,3600],{"className":3599},[788],[572,3601,3603],{"className":3602,"style":908},[792],[572,3604,3605,3608],{"style":932},[572,3606],{"className":3607,"style":936},[800],[572,3609,3611],{"className":3610},[805,806,807,808],[572,3612,740],{"className":3613},[615,808],[572,3615],{"className":3616,"style":1205},[893],[572,3618,1146],{"className":3619},[1209],[572,3621],{"className":3622,"style":1205},[893],[572,3624,3626,3629],{"className":3625},[606],[572,3627],{"className":3628,"style":2126},[610],[572,3630,2171],{"className":3631},[615],[572,3633,3635,3659],{"className":3634},[575],[572,3636,3638],{"className":3637},[579],[581,3639,3640],{"xmlns":583},[585,3641,3642,3656],{},[588,3643,3644,3650,3652,3654],{},[734,3645,3646,3648],{},[591,3647,639],{},[641,3649,970],{"mathvariant":968,"lspace":969,"rspace":969},[641,3651,743],{},[730,3653,740],{},[591,3655,593],{},[595,3657,3658],{"encoding":597},"v' = 2x",[572,3660,3662,3709],{"className":3661,"ariaHidden":602},[601],[572,3663,3665,3668,3700,3703,3706],{"className":3664},[606],[572,3666],{"className":3667,"style":1025},[610],[572,3669,3671,3674],{"className":3670},[615],[572,3672,639],{"className":3673,"style":666},[615,616],[572,3675,3677],{"className":3676},[821],[572,3678,3680],{"className":3679},[783],[572,3681,3683],{"className":3682},[788],[572,3684,3686],{"className":3685,"style":1025},[792],[572,3687,3688,3691],{"style":932},[572,3689],{"className":3690,"style":936},[800],[572,3692,3694],{"className":3693},[805,806,807,808],[572,3695,3697],{"className":3696},[615,808],[572,3698,970],{"className":3699},[615,808],[572,3701],{"className":3702,"style":894},[893],[572,3704,743],{"className":3705},[898],[572,3707],{"className":3708,"style":894},[893],[572,3710,3712,3715,3718],{"className":3711},[606],[572,3713],{"className":3714,"style":2126},[610],[572,3716,740],{"className":3717},[615],[572,3719,593],{"className":3720},[615,616],[572,3722,3724],{"className":3723},[1247],[572,3725,3727,3841],{"className":3726},[575],[572,3728,3730],{"className":3729},[579],[581,3731,3732],{"xmlns":583,"display":1256},[585,3733,3734,3838],{},[588,3735,3736,3742,3744,3746,3748,3750,3802,3804],{},[734,3737,3738,3740],{},[591,3739,693],{},[641,3741,970],{"mathvariant":968,"lspace":969,"rspace":969},[641,3743,644],{"stretchy":643},[591,3745,593],{},[641,3747,649],{"stretchy":643},[641,3749,743],{},[727,3751,3752,3782],{},[588,3753,3754,3756,3758,3760,3766,3768,3770,3772,3774,3776,3778,3780],{},[730,3755,2171],{},[641,3757,1358],{},[641,3759,644],{"stretchy":643},[734,3761,3762,3764],{},[591,3763,593],{},[730,3765,740],{},[641,3767,1146],{},[730,3769,2171],{},[641,3771,649],{"stretchy":643},[641,3773,754],{},[591,3775,593],{},[641,3777,1358],{},[730,3779,740],{},[591,3781,593],{},[588,3783,3784,3786,3792,3794,3796],{},[641,3785,644],{"stretchy":643},[734,3787,3788,3790],{},[591,3789,593],{},[730,3791,740],{},[641,3793,1146],{},[730,3795,2171],{},[734,3797,3798,3800],{},[641,3799,649],{"stretchy":643},[730,3801,740],{},[641,3803,743],{},[727,3805,3806,3818],{},[588,3807,3808,3810,3812],{},[730,3809,2171],{},[641,3811,754],{},[734,3813,3814,3816],{},[591,3815,593],{},[730,3817,740],{},[588,3819,3820,3822,3828,3830,3832],{},[641,3821,644],{"stretchy":643},[734,3823,3824,3826],{},[591,3825,593],{},[730,3827,740],{},[641,3829,1146],{},[730,3831,2171],{},[734,3833,3834,3836],{},[641,3835,649],{"stretchy":643},[730,3837,740],{},[595,3839,3840],{"encoding":597},"f'(x) = \\frac{1 \\cdot (x^2 + 1) - x \\cdot 2x}{(x^2 + 1)^2} = \\frac{1 - x^2}{(x^2 + 1)^2}",[572,3842,3844,3900,4132],{"className":3843,"ariaHidden":602},[601],[572,3845,3847,3850,3882,3885,3888,3891,3894,3897],{"className":3846},[606],[572,3848],{"className":3849,"style":2840},[610],[572,3851,3853,3856],{"className":3852},[615],[572,3854,693],{"className":3855,"style":709},[615,616],[572,3857,3859],{"className":3858},[821],[572,3860,3862],{"className":3861},[783],[572,3863,3865],{"className":3864},[788],[572,3866,3868],{"className":3867,"style":2859},[792],[572,3869,3870,3873],{"style":2862},[572,3871],{"className":3872,"style":936},[800],[572,3874,3876],{"className":3875},[805,806,807,808],[572,3877,3879],{"className":3878},[615,808],[572,3880,970],{"className":3881},[615,808],[572,3883,644],{"className":3884},[670],[572,3886,593],{"className":3887},[615,616],[572,3889,649],{"className":3890},[677],[572,3892],{"className":3893,"style":894},[893],[572,3895,743],{"className":3896},[898],[572,3898],{"className":3899,"style":894},[893],[572,3901,3903,3907,4123,4126,4129],{"className":3902},[606],[572,3904],{"className":3905,"style":3906},[610],"height:2.4271em;vertical-align:-0.936em;",[572,3908,3910,3913,4120],{"className":3909},[615],[572,3911],{"className":3912},[670,776],[572,3914,3916],{"className":3915},[727],[572,3917,3919,4112],{"className":3918},[783,784],[572,3920,3922,4109],{"className":3921},[788],[572,3923,3926,4007,4015],{"className":3924,"style":3925},[792],"height:1.4911em;",[572,3927,3928,3931],{"style":2921},[572,3929],{"className":3930,"style":801},[800],[572,3932,3934,3937,3966,3969,3972,3975,3978],{"className":3933},[615],[572,3935,644],{"className":3936},[670],[572,3938,3940,3943],{"className":3939},[615],[572,3941,593],{"className":3942},[615,616],[572,3944,3946],{"className":3945},[821],[572,3947,3949],{"className":3948},[783],[572,3950,3952],{"className":3951},[788],[572,3953,3955],{"className":3954,"style":2964},[792],[572,3956,3957,3960],{"style":2967},[572,3958],{"className":3959,"style":936},[800],[572,3961,3963],{"className":3962},[805,806,807,808],[572,3964,740],{"className":3965},[615,808],[572,3967],{"className":3968,"style":1205},[893],[572,3970,1146],{"className":3971},[1209],[572,3973],{"className":3974,"style":1205},[893],[572,3976,2171],{"className":3977},[615],[572,3979,3981,3984],{"className":3980},[677],[572,3982,649],{"className":3983},[677],[572,3985,3987],{"className":3986},[821],[572,3988,3990],{"className":3989},[783],[572,3991,3993],{"className":3992},[788],[572,3994,3996],{"className":3995,"style":2964},[792],[572,3997,3998,4001],{"style":2967},[572,3999],{"className":4000,"style":936},[800],[572,4002,4004],{"className":4003},[805,806,807,808],[572,4005,740],{"className":4006},[615,808],[572,4008,4009,4012],{"style":849},[572,4010],{"className":4011,"style":801},[800],[572,4013],{"className":4014,"style":857},[856],[572,4016,4017,4020],{"style":2987},[572,4018],{"className":4019,"style":801},[800],[572,4021,4023,4026,4029,4032,4035,4038,4067,4070,4073,4076,4079,4082,4085,4088,4091,4094,4097,4100,4103,4106],{"className":4022},[615],[572,4024,2171],{"className":4025},[615],[572,4027],{"className":4028,"style":1205},[893],[572,4030,1358],{"className":4031},[1209],[572,4033],{"className":4034,"style":1205},[893],[572,4036,644],{"className":4037},[670],[572,4039,4041,4044],{"className":4040},[615],[572,4042,593],{"className":4043},[615,616],[572,4045,4047],{"className":4046},[821],[572,4048,4050],{"className":4049},[783],[572,4051,4053],{"className":4052},[788],[572,4054,4056],{"className":4055,"style":908},[792],[572,4057,4058,4061],{"style":932},[572,4059],{"className":4060,"style":936},[800],[572,4062,4064],{"className":4063},[805,806,807,808],[572,4065,740],{"className":4066},[615,808],[572,4068],{"className":4069,"style":1205},[893],[572,4071,1146],{"className":4072},[1209],[572,4074],{"className":4075,"style":1205},[893],[572,4077,2171],{"className":4078},[615],[572,4080,649],{"className":4081},[677],[572,4083],{"className":4084,"style":1205},[893],[572,4086,754],{"className":4087},[1209],[572,4089],{"className":4090,"style":1205},[893],[572,4092,593],{"className":4093},[615,616],[572,4095],{"className":4096,"style":1205},[893],[572,4098,1358],{"className":4099},[1209],[572,4101],{"className":4102,"style":1205},[893],[572,4104,740],{"className":4105},[615],[572,4107,593],{"className":4108},[615,616],[572,4110,877],{"className":4111},[876],[572,4113,4115],{"className":4114},[788],[572,4116,4118],{"className":4117,"style":2066},[792],[572,4119],{},[572,4121],{"className":4122},[677,776],[572,4124],{"className":4125,"style":894},[893],[572,4127,743],{"className":4128},[898],[572,4130],{"className":4131,"style":894},[893],[572,4133,4135,4138],{"className":4134},[606],[572,4136],{"className":4137,"style":3906},[610],[572,4139,4141,4144,4305],{"className":4140},[615],[572,4142],{"className":4143},[670,776],[572,4145,4147],{"className":4146},[727],[572,4148,4150,4297],{"className":4149},[783,784],[572,4151,4153,4294],{"className":4152},[788],[572,4154,4156,4237,4245],{"className":4155,"style":3925},[792],[572,4157,4158,4161],{"style":2921},[572,4159],{"className":4160,"style":801},[800],[572,4162,4164,4167,4196,4199,4202,4205,4208],{"className":4163},[615],[572,4165,644],{"className":4166},[670],[572,4168,4170,4173],{"className":4169},[615],[572,4171,593],{"className":4172},[615,616],[572,4174,4176],{"className":4175},[821],[572,4177,4179],{"className":4178},[783],[572,4180,4182],{"className":4181},[788],[572,4183,4185],{"className":4184,"style":2964},[792],[572,4186,4187,4190],{"style":2967},[572,4188],{"className":4189,"style":936},[800],[572,4191,4193],{"className":4192},[805,806,807,808],[572,4194,740],{"className":4195},[615,808],[572,4197],{"className":4198,"style":1205},[893],[572,4200,1146],{"className":4201},[1209],[572,4203],{"className":4204,"style":1205},[893],[572,4206,2171],{"className":4207},[615],[572,4209,4211,4214],{"className":4210},[677],[572,4212,649],{"className":4213},[677],[572,4215,4217],{"className":4216},[821],[572,4218,4220],{"className":4219},[783],[572,4221,4223],{"className":4222},[788],[572,4224,4226],{"className":4225,"style":2964},[792],[572,4227,4228,4231],{"style":2967},[572,4229],{"className":4230,"style":936},[800],[572,4232,4234],{"className":4233},[805,806,807,808],[572,4235,740],{"className":4236},[615,808],[572,4238,4239,4242],{"style":849},[572,4240],{"className":4241,"style":801},[800],[572,4243],{"className":4244,"style":857},[856],[572,4246,4247,4250],{"style":2987},[572,4248],{"className":4249,"style":801},[800],[572,4251,4253,4256,4259,4262,4265],{"className":4252},[615],[572,4254,2171],{"className":4255},[615],[572,4257],{"className":4258,"style":1205},[893],[572,4260,754],{"className":4261},[1209],[572,4263],{"className":4264,"style":1205},[893],[572,4266,4268,4271],{"className":4267},[615],[572,4269,593],{"className":4270},[615,616],[572,4272,4274],{"className":4273},[821],[572,4275,4277],{"className":4276},[783],[572,4278,4280],{"className":4279},[788],[572,4281,4283],{"className":4282,"style":908},[792],[572,4284,4285,4288],{"style":932},[572,4286],{"className":4287,"style":936},[800],[572,4289,4291],{"className":4290},[805,806,807,808],[572,4292,740],{"className":4293},[615,808],[572,4295,877],{"className":4296},[876],[572,4298,4300],{"className":4299},[788],[572,4301,4303],{"className":4302,"style":2066},[792],[572,4304],{},[572,4306],{"className":4307},[677,776],[559,4309,4311],{"id":4310},"typische-fehler","Typische Fehler",[4313,4314,4315,4448,4451,4776],"ul",{},[4316,4317,4318,4319,4447],"li",{},"Die Reihenfolge im Zähler vertauschen. ",[572,4320,4322,4352],{"className":4321},[575],[572,4323,4325],{"className":4324},[579],[581,4326,4327],{"xmlns":583},[585,4328,4329,4349],{},[588,4330,4331,4333,4339,4341,4347],{},[591,4332,1129],{},[734,4334,4335,4337],{},[591,4336,639],{},[641,4338,970],{"mathvariant":968,"lspace":969,"rspace":969},[641,4340,754],{},[734,4342,4343,4345],{},[591,4344,1129],{},[641,4346,970],{"mathvariant":968,"lspace":969,"rspace":969},[591,4348,639],{},[595,4350,4351],{"encoding":597},"uv' - u'v",[572,4353,4355,4406],{"className":4354,"ariaHidden":602},[601],[572,4356,4358,4362,4365,4397,4400,4403],{"className":4357},[606],[572,4359],{"className":4360,"style":4361},[610],"height:0.8352em;vertical-align:-0.0833em;",[572,4363,1129],{"className":4364},[615,616],[572,4366,4368,4371],{"className":4367},[615],[572,4369,639],{"className":4370,"style":666},[615,616],[572,4372,4374],{"className":4373},[821],[572,4375,4377],{"className":4376},[783],[572,4378,4380],{"className":4379},[788],[572,4381,4383],{"className":4382,"style":1025},[792],[572,4384,4385,4388],{"style":932},[572,4386],{"className":4387,"style":936},[800],[572,4389,4391],{"className":4390},[805,806,807,808],[572,4392,4394],{"className":4393},[615,808],[572,4395,970],{"className":4396},[615,808],[572,4398],{"className":4399,"style":1205},[893],[572,4401,754],{"className":4402},[1209],[572,4404],{"className":4405,"style":1205},[893],[572,4407,4409,4412,4444],{"className":4408},[606],[572,4410],{"className":4411,"style":1025},[610],[572,4413,4415,4418],{"className":4414},[615],[572,4416,1129],{"className":4417},[615,616],[572,4419,4421],{"className":4420},[821],[572,4422,4424],{"className":4423},[783],[572,4425,4427],{"className":4426},[788],[572,4428,4430],{"className":4429,"style":1025},[792],[572,4431,4432,4435],{"style":932},[572,4433],{"className":4434,"style":936},[800],[572,4436,4438],{"className":4437},[805,806,807,808],[572,4439,4441],{"className":4440},[615,808],[572,4442,970],{"className":4443},[615,808],[572,4445,639],{"className":4446,"style":666},[615,616]," liefert das falsche Vorzeichen, weil hier minus steht.",[4316,4449,4450],{},"Das Quadrat im Nenner vergessen.",[4316,4452,4453,4454,4775],{},"Zähler und Nenner einzeln ableiten: ",[572,4455,4457,4501],{"className":4456},[575],[572,4458,4460],{"className":4459},[579],[581,4461,4462],{"xmlns":583},[585,4463,4464,4498],{},[588,4465,4466,4482,4484],{},[734,4467,4468,4480],{},[588,4469,4470,4472,4478],{},[641,4471,644],{"fence":602},[727,4473,4474,4476],{},[591,4475,1129],{},[591,4477,639],{},[641,4479,649],{"fence":602},[641,4481,970],{"mathvariant":968,"lspace":969,"rspace":969},[641,4483,743],{},[727,4485,4486,4492],{},[734,4487,4488,4490],{},[591,4489,1129],{},[641,4491,970],{"mathvariant":968,"lspace":969,"rspace":969},[734,4493,4494,4496],{},[591,4495,639],{},[641,4497,970],{"mathvariant":968,"lspace":969,"rspace":969},[595,4499,4500],{"encoding":597},"\\left(\\frac{u}{v}\\right)' = \\frac{u'}{v'}",[572,4502,4504,4638],{"className":4503,"ariaHidden":602},[601],[572,4505,4507,4511,4629,4632,4635],{"className":4506},[606],[572,4508],{"className":4509,"style":4510},[610],"height:1.3418em;vertical-align:-0.35em;",[572,4512,4515,4601],{"className":4513},[4514],"minner",[572,4516,4518,4527,4595],{"className":4517},[4514],[572,4519,4523],{"className":4520,"style":4522},[670,4521],"delimcenter","top:0em;",[572,4524,644],{"className":4525},[4526,843],"delimsizing",[572,4528,4530,4533,4592],{"className":4529},[615],[572,4531],{"className":4532},[670,776],[572,4534,4536],{"className":4535},[727],[572,4537,4539,4584],{"className":4538},[783,784],[572,4540,4542,4581],{"className":4541},[788],[572,4543,4545,4559,4567],{"className":4544,"style":3310},[792],[572,4546,4547,4550],{"style":796},[572,4548],{"className":4549,"style":801},[800],[572,4551,4553],{"className":4552},[805,806,807,808],[572,4554,4556],{"className":4555},[615,808],[572,4557,639],{"className":4558,"style":666},[615,616,808],[572,4560,4561,4564],{"style":849},[572,4562],{"className":4563,"style":801},[800],[572,4565],{"className":4566,"style":857},[856],[572,4568,4569,4572],{"style":860},[572,4570],{"className":4571,"style":801},[800],[572,4573,4575],{"className":4574},[805,806,807,808],[572,4576,4578],{"className":4577},[615,808],[572,4579,1129],{"className":4580},[615,616,808],[572,4582,877],{"className":4583},[876],[572,4585,4587],{"className":4586},[788],[572,4588,4590],{"className":4589,"style":884},[792],[572,4591],{},[572,4593],{"className":4594},[677,776],[572,4596,4598],{"className":4597,"style":4522},[677,4521],[572,4599,649],{"className":4600},[4526,843],[572,4602,4604],{"className":4603},[821],[572,4605,4607],{"className":4606},[783],[572,4608,4610],{"className":4609},[788],[572,4611,4614],{"className":4612,"style":4613},[792],"height:0.9918em;",[572,4615,4617,4620],{"style":4616},"top:-3.3029em;margin-right:0.05em;",[572,4618],{"className":4619,"style":936},[800],[572,4621,4623],{"className":4622},[805,806,807,808],[572,4624,4626],{"className":4625},[615,808],[572,4627,970],{"className":4628},[615,808],[572,4630],{"className":4631,"style":894},[893],[572,4633,743],{"className":4634},[898],[572,4636],{"className":4637,"style":894},[893],[572,4639,4641,4645],{"className":4640},[606],[572,4642],{"className":4643,"style":4644},[610],"height:1.3185em;vertical-align:-0.345em;",[572,4646,4648,4651,4772],{"className":4647},[615],[572,4649],{"className":4650},[670,776],[572,4652,4654],{"className":4653},[727],[572,4655,4657,4764],{"className":4656},[783,784],[572,4658,4660,4761],{"className":4659},[788],[572,4661,4664,4708,4716],{"className":4662,"style":4663},[792],"height:0.9735em;",[572,4665,4666,4669],{"style":796},[572,4667],{"className":4668,"style":801},[800],[572,4670,4672],{"className":4671},[805,806,807,808],[572,4673,4675],{"className":4674},[615,808],[572,4676,4678,4681],{"className":4677},[615,808],[572,4679,639],{"className":4680,"style":666},[615,616,808],[572,4682,4684],{"className":4683},[821],[572,4685,4687],{"className":4686},[783],[572,4688,4690],{"className":4689},[788],[572,4691,4694],{"className":4692,"style":4693},[792],"height:0.6828em;",[572,4695,4696,4699],{"style":834},[572,4697],{"className":4698,"style":838},[800],[572,4700,4702],{"className":4701},[805,842,843,808],[572,4703,4705],{"className":4704},[615,808],[572,4706,970],{"className":4707},[615,808],[572,4709,4710,4713],{"style":849},[572,4711],{"className":4712,"style":801},[800],[572,4714],{"className":4715,"style":857},[856],[572,4717,4718,4721],{"style":860},[572,4719],{"className":4720,"style":801},[800],[572,4722,4724],{"className":4723},[805,806,807,808],[572,4725,4727],{"className":4726},[615,808],[572,4728,4730,4733],{"className":4729},[615,808],[572,4731,1129],{"className":4732},[615,616,808],[572,4734,4736],{"className":4735},[821],[572,4737,4739],{"className":4738},[783],[572,4740,4742],{"className":4741},[788],[572,4743,4746],{"className":4744,"style":4745},[792],"height:0.8278em;",[572,4747,4749,4752],{"style":4748},"top:-2.931em;margin-right:0.0714em;",[572,4750],{"className":4751,"style":838},[800],[572,4753,4755],{"className":4754},[805,842,843,808],[572,4756,4758],{"className":4757},[615,808],[572,4759,970],{"className":4760},[615,808],[572,4762,877],{"className":4763},[876],[572,4765,4767],{"className":4766},[788],[572,4768,4770],{"className":4769,"style":884},[792],[572,4771],{},[572,4773],{"className":4774},[677,776]," ist falsch.",[4316,4777,4778,4779,4845],{},"Beim Ausmultiplizieren im Zähler die Klammer um ",[572,4780,4782,4806],{"className":4781},[575],[572,4783,4785],{"className":4784},[579],[581,4786,4787],{"xmlns":583},[585,4788,4789,4803],{},[588,4790,4791,4793,4795,4797,4799,4801],{},[641,4792,644],{"stretchy":643},[730,4794,740],{},[591,4796,593],{},[641,4798,1146],{},[730,4800,2171],{},[641,4802,649],{"stretchy":643},[595,4804,4805],{"encoding":597},"(2x + 1)",[572,4807,4809,4833],{"className":4808,"ariaHidden":602},[601],[572,4810,4812,4815,4818,4821,4824,4827,4830],{"className":4811},[606],[572,4813],{"className":4814,"style":662},[610],[572,4816,644],{"className":4817},[670],[572,4819,740],{"className":4820},[615],[572,4822,593],{"className":4823},[615,616],[572,4825],{"className":4826,"style":1205},[893],[572,4828,1146],{"className":4829},[1209],[572,4831],{"className":4832,"style":1205},[893],[572,4834,4836,4839,4842],{"className":4835},[606],[572,4837],{"className":4838,"style":662},[610],[572,4840,2171],{"className":4841},[615],[572,4843,649],{"className":4844},[677]," weglassen, dann geht das Minus nur an den ersten Summanden.",{"title":4847,"searchDepth":4848,"depth":4848,"links":4849},"",2,[4850,4851,4852,4853],{"id":561,"depth":4848,"text":562},{"id":1108,"depth":4848,"text":1109},{"id":2133,"depth":4848,"text":2134},{"id":4310,"depth":4848,"text":4311},[4855,4858,4861,4865,4868,4870],{"lhs":4856,"rhs":4857},"(u1\u002Fv1 - u0\u002Fv0)\u002Fh","(((u1 - u0)\u002Fh)*v0 - u0*((v1 - v0)\u002Fh))\u002F(v1*v0)",{"lhs":4859,"rhs":4860},"(2*(x - 3) - (2*x + 1)*1)\u002F(x - 3)^2","-7\u002F(x - 3)^2",{"lhs":4862,"rhs":2094,"where":4863},"round(((2*(x+1e-5) + 1)\u002F((x+1e-5) - 3) - (2*(x-1e-5) + 1)\u002F((x-1e-5) - 3))\u002F(2e-5) + 7\u002F(x - 3)^2, 6)",{"x":4864},1,{"lhs":4866,"rhs":4867},"(1*(x^2 + 1) - x*2*x)\u002F(x^2 + 1)^2","(1 - x^2)\u002F(x^2 + 1)^2",{"lhs":4869,"rhs":2094},"round(((x+1e-5)\u002F((x+1e-5)^2 + 1) - (x-1e-5)\u002F((x-1e-5)^2 + 1))\u002F(2e-5) - (1 - x^2)\u002F(x^2 + 1)^2, 6)",{"lhs":4871,"rhs":4872},"(0*x^2 - 3*2*x)\u002F(x^2)^2","-6*x^(-3)","u, v \\text{ differenzierbar},\\ v(x) \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>u\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>v\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">u, v\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">differenzierbar\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>v\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">v(x) \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","quotient-rule","f(x) = \\frac{u(x)}{v(x)} \\;\\Rightarrow\\; f'(x) = \\frac{u'(x) \\cdot v(x) - u(x) \\cdot v'(x)}{\\big(v(x)\\big)^2}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>u\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>v\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsup>\u003Cmi>u\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>v\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>u\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmi>v\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmo fence=\"false\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">(\u003C\u002Fmo>\u003Cmi>v\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmsup>\u003Cmo fence=\"false\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">)\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x) = \\frac{u(x)}{v(x)} \\;\\Rightarrow\\; f'(x) = \\frac{u'(x) \\cdot v(x) - u(x) \\cdot v'(x)}{\\big(v(x)\\big)^2}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.363em;vertical-align:-0.936em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.427em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.936em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0519em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.7229em;vertical-align:-1.294em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4289em;\">\u003Cspan style=\"top:-2.11em;\">\u003Cspan class=\"pstrut\" style=\"height:3.054em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.054em;\">\u003Cspan style=\"top:-3.3029em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.284em;\">\u003Cspan class=\"pstrut\" style=\"height:3.054em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.731em;\">\u003Cspan class=\"pstrut\" style=\"height:3.054em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.294em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fquotientenregel",[],[4886,4887,4888],"product-rule","chain-rule","power-rule",{"title":548,"description":4847},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fquotientenregel","Einen Bruch leitet man ab mit Zähler abgeleitet mal Nenner minus Zähler mal Nenner abgeleitet, geteilt durch Nenner².",[4893,4894,4895,4896],"ableitung","ableitungsregel","quotient","bruch",[4898,4901,4904,4908],{"symbol":1129,"meaning":4899,"symbolHtml":4900},"Zählerfunktion","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>u\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">u\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":639,"meaning":4902,"symbolHtml":4903},"Nennerfunktion, darf an der Stelle x nicht null sein","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>v\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">v\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4905,"meaning":4906,"symbolHtml":4907},"u'(x), v'(x)","Ableitungen von Zähler und Nenner","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>u\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsup>\u003Cmi>v\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">u'(x), v'(x)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0019em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4909,"meaning":4910,"symbolHtml":4911},"f'(x)","Ableitung des Quotienten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f'(x)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0019em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","KdaPtTZjnevwsNBIuRaBfvaq3lQYcHuKowBHPwe1CuY",[4914,4917,4920],{"stem":4915,"title":4916,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fkettenregel","Kettenregel",{"stem":4918,"title":4919,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fpotenzregel","Potenzregel",{"stem":4921,"title":4922,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fproduktregel","Produktregel",1793824283366]