[{"data":1,"prerenderedAt":4102},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-tangens":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-tangens":4089},[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":4031,"conditions":4052,"conditionsHtml":4053,"deprecated":4054,"description":4024,"extension":4055,"figure":4054,"figureCaption":4054,"figureHtml":4054,"formulaId":4056,"latex":4057,"latexHtml":4058,"level":4059,"meta":4060,"navigation":4061,"path":4062,"redirectFrom":4063,"related":4064,"seo":4069,"stem":4070,"subject":577,"summary":4071,"tags":4072,"variables":4077,"__hash__":4088},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-tangens.md","Ableitung des Tangens",[550,551,552,553,554],"tan x ableiten","Ableitung tan","Ableitung Tangensfunktion","1 durch cos hoch 2","1 + tan^2",{"type":556,"value":557,"toc":4023},"minimark",[558,563,772,1233,1237,1418,1993,2190,2194,2544,2973,2976,3294,3298],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,771],"p",{},"Der Tangens ist an allen Stellen differenzierbar, an denen er definiert ist, also überall außer bei ",[568,569,572,617],"span",{"className":570},[571],"katex",[568,573,576],{"className":574},[575],"katex-mathml",[577,578,580],"math",{"xmlns":579},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[581,582,583,612],"semantics",{},[584,585,586,590,594,604,607,610],"mrow",{},[587,588,589],"mi",{},"x",[591,592,593],"mo",{},"=",[595,596,597,600],"mfrac",{},[587,598,599],{},"π",[601,602,603],"mn",{},"2",[591,605,606],{},"+",[587,608,609],{},"k",[587,611,599],{},[613,614,616],"annotation",{"encoding":615},"application\u002Fx-tex","x = \\frac{\\pi}{2} + k\\pi",[568,618,622,648,757],{"className":619,"ariaHidden":621},[620],"katex-html","true",[568,623,626,631,636,641,645],{"className":624},[625],"base",[568,627],{"className":628,"style":630},[629],"strut","height:0.4306em;",[568,632,589],{"className":633},[634,635],"mord","mathnormal",[568,637],{"className":638,"style":640},[639],"mspace","margin-right:0.2778em;",[568,642,593],{"className":643},[644],"mrel",[568,646],{"className":647,"style":640},[639],[568,649,651,655,746,750,754],{"className":650},[625],[568,652],{"className":653,"style":654},[629],"height:1.0404em;vertical-align:-0.345em;",[568,656,658,663,742],{"className":657},[634],[568,659],{"className":660},[661,662],"mopen","nulldelimiter",[568,664,666],{"className":665},[595],[568,667,671,733],{"className":668},[669,670],"vlist-t","vlist-t2",[568,672,675,728],{"className":673},[674],"vlist-r",[568,676,680,701,712],{"className":677,"style":679},[678],"vlist","height:0.6954em;",[568,681,683,688],{"style":682},"top:-2.655em;",[568,684],{"className":685,"style":687},[686],"pstrut","height:3em;",[568,689,695],{"className":690},[691,692,693,694],"sizing","reset-size6","size3","mtight",[568,696,698],{"className":697},[634,694],[568,699,603],{"className":700},[634,694],[568,702,704,707],{"style":703},"top:-3.23em;",[568,705],{"className":706,"style":687},[686],[568,708],{"className":709,"style":711},[710],"frac-line","border-bottom-width:0.04em;",[568,713,715,718],{"style":714},"top:-3.394em;",[568,716],{"className":717,"style":687},[686],[568,719,721],{"className":720},[691,692,693,694],[568,722,724],{"className":723},[634,694],[568,725,599],{"className":726,"style":727},[634,635,694],"margin-right:0.0359em;",[568,729,732],{"className":730},[731],"vlist-s","​",[568,734,736],{"className":735},[674],[568,737,740],{"className":738,"style":739},[678],"height:0.345em;",[568,741],{},[568,743],{"className":744},[745,662],"mclose",[568,747],{"className":748,"style":749},[639],"margin-right:0.2222em;",[568,751,606],{"className":752},[753],"mbin",[568,755],{"className":756,"style":749},[639],[568,758,760,764,768],{"className":759},[625],[568,761],{"className":762,"style":763},[629],"height:0.6944em;",[568,765,609],{"className":766,"style":767},[634,635],"margin-right:0.0315em;",[568,769,599],{"className":770,"style":727},[634,635],". Dort hat der Graph senkrechte Asymptoten.",[564,773,774,775,947,948,1134,1135,1232],{},"Beide Formen der Ableitung sind gleichwertig, wegen ",[568,776,778,825],{"className":777},[571],[568,779,781],{"className":780},[575],[577,782,783],{"xmlns":579},[581,784,785,822],{},[584,786,787,800,802,804,815,817,819],{},[788,789,790,798],"msup",{},[584,791,792,795],{},[587,793,794],{},"sin",[591,796,797],{},"⁡",[601,799,603],{},[587,801,589],{},[591,803,606],{},[788,805,806,813],{},[584,807,808,811],{},[587,809,810],{},"cos",[591,812,797],{},[601,814,603],{},[587,816,589],{},[591,818,593],{},[601,820,821],{},"1",[613,823,824],{"encoding":615},"\\sin^2 x + \\cos^2 x = 1",[568,826,828,885,937],{"className":827,"ariaHidden":621},[620],[568,829,831,835,869,873,876,879,882],{"className":830},[625],[568,832],{"className":833,"style":834},[629],"height:0.9552em;vertical-align:-0.0833em;",[568,836,839,842],{"className":837},[838],"mop",[568,840,794],{"className":841},[838],[568,843,846],{"className":844},[845],"msupsub",[568,847,849],{"className":848},[669],[568,850,852],{"className":851},[674],[568,853,856],{"className":854,"style":855},[678],"height:0.8719em;",[568,857,859,863],{"style":858},"top:-3.1208em;margin-right:0.05em;",[568,860],{"className":861,"style":862},[686],"height:2.7em;",[568,864,866],{"className":865},[691,692,693,694],[568,867,603],{"className":868},[634,694],[568,870],{"className":871,"style":872},[639],"margin-right:0.1667em;",[568,874,589],{"className":875},[634,635],[568,877],{"className":878,"style":749},[639],[568,880,606],{"className":881},[753],[568,883],{"className":884,"style":749},[639],[568,886,888,892,922,925,928,931,934],{"className":887},[625],[568,889],{"className":890,"style":891},[629],"height:0.8141em;",[568,893,895,898],{"className":894},[838],[568,896,810],{"className":897},[838],[568,899,901],{"className":900},[845],[568,902,904],{"className":903},[669],[568,905,907],{"className":906},[674],[568,908,910],{"className":909,"style":891},[678],[568,911,913,916],{"style":912},"top:-3.063em;margin-right:0.05em;",[568,914],{"className":915,"style":862},[686],[568,917,919],{"className":918},[691,692,693,694],[568,920,603],{"className":921},[634,694],[568,923],{"className":924,"style":872},[639],[568,926,589],{"className":927},[634,635],[568,929],{"className":930,"style":640},[639],[568,932,593],{"className":933},[644],[568,935],{"className":936,"style":640},[639],[568,938,940,944],{"className":939},[625],[568,941],{"className":942,"style":943},[629],"height:0.6444em;",[568,945,821],{"className":946},[634],". Da ",[568,949,951,987],{"className":950},[571],[568,952,954],{"className":953},[575],[577,955,956],{"xmlns":579},[581,957,958,984],{},[584,959,960,978,981],{},[595,961,962,964],{},[601,963,821],{},[584,965,966,976],{},[788,967,968,974],{},[584,969,970,972],{},[587,971,810],{},[591,973,797],{},[601,975,603],{},[587,977,589],{},[591,979,980],{},">",[601,982,983],{},"0",[613,985,986],{"encoding":615},"\\frac{1}{\\cos^2 x} > 0",[568,988,990,1125],{"className":989,"ariaHidden":621},[620],[568,991,993,997,1116,1119,1122],{"className":992},[625],[568,994],{"className":995,"style":996},[629],"height:1.1901em;vertical-align:-0.345em;",[568,998,1000,1003,1113],{"className":999},[634],[568,1001],{"className":1002},[661,662],[568,1004,1006],{"className":1005},[595],[568,1007,1009,1105],{"className":1008},[669,670],[568,1010,1012,1102],{"className":1011},[674],[568,1013,1016,1080,1088],{"className":1014,"style":1015},[678],"height:0.8451em;",[568,1017,1018,1021],{"style":682},[568,1019],{"className":1020,"style":687},[686],[568,1022,1024],{"className":1023},[691,692,693,694],[568,1025,1027,1073,1077],{"className":1026},[634,694],[568,1028,1030,1045],{"className":1029},[838,694],[568,1031,1033,1037,1041],{"className":1032},[838,694],[568,1034,1036],{"className":1035},[694],"c",[568,1038,1040],{"className":1039},[694],"o",[568,1042,1044],{"className":1043},[694],"s",[568,1046,1048],{"className":1047},[845],[568,1049,1051],{"className":1050},[669],[568,1052,1054],{"className":1053},[674],[568,1055,1058],{"className":1056,"style":1057},[678],"height:0.7463em;",[568,1059,1061,1065],{"style":1060},"top:-2.786em;margin-right:0.0714em;",[568,1062],{"className":1063,"style":1064},[686],"height:2.5em;",[568,1066,1070],{"className":1067},[691,1068,1069,694],"reset-size3","size1",[568,1071,603],{"className":1072},[634,694],[568,1074],{"className":1075,"style":1076},[639,694],"margin-right:0.1952em;",[568,1078,589],{"className":1079},[634,635,694],[568,1081,1082,1085],{"style":703},[568,1083],{"className":1084,"style":687},[686],[568,1086],{"className":1087,"style":711},[710],[568,1089,1090,1093],{"style":714},[568,1091],{"className":1092,"style":687},[686],[568,1094,1096],{"className":1095},[691,692,693,694],[568,1097,1099],{"className":1098},[634,694],[568,1100,821],{"className":1101},[634,694],[568,1103,732],{"className":1104},[731],[568,1106,1108],{"className":1107},[674],[568,1109,1111],{"className":1110,"style":739},[678],[568,1112],{},[568,1114],{"className":1115},[745,662],[568,1117],{"className":1118,"style":640},[639],[568,1120,980],{"className":1121},[644],[568,1123],{"className":1124,"style":640},[639],[568,1126,1128,1131],{"className":1127},[625],[568,1129],{"className":1130,"style":943},[629],[568,1132,983],{"className":1133},[634]," ist, ist der Tangens auf jedem Intervall zwischen zwei Polstellen streng monoton wachsend. Die Form ",[568,1136,1138,1167],{"className":1137},[571],[568,1139,1141],{"className":1140},[575],[577,1142,1143],{"xmlns":579},[581,1144,1145,1164],{},[584,1146,1147,1149,1151,1162],{},[601,1148,821],{},[591,1150,606],{},[788,1152,1153,1160],{},[584,1154,1155,1158],{},[587,1156,1157],{},"tan",[591,1159,797],{},[601,1161,603],{},[587,1163,589],{},[613,1165,1166],{"encoding":615},"1 + \\tan^2 x",[568,1168,1170,1189],{"className":1169,"ariaHidden":621},[620],[568,1171,1173,1177,1180,1183,1186],{"className":1172},[625],[568,1174],{"className":1175,"style":1176},[629],"height:0.7278em;vertical-align:-0.0833em;",[568,1178,821],{"className":1179},[634],[568,1181],{"className":1182,"style":749},[639],[568,1184,606],{"className":1185},[753],[568,1187],{"className":1188,"style":749},[639],[568,1190,1192,1196,1226,1229],{"className":1191},[625],[568,1193],{"className":1194,"style":1195},[629],"height:0.8191em;",[568,1197,1199,1202],{"className":1198},[838],[568,1200,1157],{"className":1201},[838],[568,1203,1205],{"className":1204},[845],[568,1206,1208],{"className":1207},[669],[568,1209,1211],{"className":1210},[674],[568,1212,1214],{"className":1213,"style":1195},[678],[568,1215,1217,1220],{"style":1216},"top:-3.068em;margin-right:0.05em;",[568,1218],{"className":1219,"style":862},[686],[568,1221,1223],{"className":1222},[691,692,693,694],[568,1224,603],{"className":1225},[634,694],[568,1227],{"className":1228,"style":872},[639],[568,1230,589],{"className":1231},[634,635]," ist praktisch, wenn man die Ableitung durch die Funktion selbst ausdrücken will, z.B. bei Differentialgleichungen oder der Ableitung des Arkustangens.",[559,1234,1236],{"id":1235},"herleitung","Herleitung",[564,1238,1239,1240,1417],{},"Mit ",[568,1241,1243,1281],{"className":1242},[571],[568,1244,1246],{"className":1245},[575],[577,1247,1248],{"xmlns":579},[581,1249,1250,1278],{},[584,1251,1252,1254,1256,1258,1260],{},[587,1253,1157],{},[591,1255,797],{},[587,1257,589],{},[591,1259,593],{},[595,1261,1262,1270],{},[584,1263,1264,1266,1268],{},[587,1265,794],{},[591,1267,797],{},[587,1269,589],{},[584,1271,1272,1274,1276],{},[587,1273,810],{},[591,1275,797],{},[587,1277,589],{},[613,1279,1280],{"encoding":615},"\\tan x = \\frac{\\sin x}{\\cos x}",[568,1282,1284,1309],{"className":1283,"ariaHidden":621},[620],[568,1285,1287,1291,1294,1297,1300,1303,1306],{"className":1286},[625],[568,1288],{"className":1289,"style":1290},[629],"height:0.6151em;",[568,1292,1157],{"className":1293},[838],[568,1295],{"className":1296,"style":872},[639],[568,1298,589],{"className":1299},[634,635],[568,1301],{"className":1302,"style":640},[639],[568,1304,593],{"className":1305},[644],[568,1307],{"className":1308,"style":640},[639],[568,1310,1312,1316],{"className":1311},[625],[568,1313],{"className":1314,"style":1315},[629],"height:1.2065em;vertical-align:-0.345em;",[568,1317,1319,1322,1414],{"className":1318},[634],[568,1320],{"className":1321},[661,662],[568,1323,1325],{"className":1324},[595],[568,1326,1328,1406],{"className":1327},[669,670],[568,1329,1331,1403],{"className":1330},[674],[568,1332,1335,1364,1372],{"className":1333,"style":1334},[678],"height:0.8615em;",[568,1336,1337,1340],{"style":682},[568,1338],{"className":1339,"style":687},[686],[568,1341,1343],{"className":1342},[691,692,693,694],[568,1344,1346,1358,1361],{"className":1345},[634,694],[568,1347,1349,1352,1355],{"className":1348},[838,694],[568,1350,1036],{"className":1351},[694],[568,1353,1040],{"className":1354},[694],[568,1356,1044],{"className":1357},[694],[568,1359],{"className":1360,"style":1076},[639,694],[568,1362,589],{"className":1363},[634,635,694],[568,1365,1366,1369],{"style":703},[568,1367],{"className":1368,"style":687},[686],[568,1370],{"className":1371,"style":711},[710],[568,1373,1374,1377],{"style":714},[568,1375],{"className":1376,"style":687},[686],[568,1378,1380],{"className":1379},[691,692,693,694],[568,1381,1383,1397,1400],{"className":1382},[634,694],[568,1384,1386,1389,1393],{"className":1385},[838,694],[568,1387,1044],{"className":1388},[694],[568,1390,1392],{"className":1391},[694],"i",[568,1394,1396],{"className":1395},[694],"n",[568,1398],{"className":1399,"style":1076},[639,694],[568,1401,589],{"className":1402},[634,635,694],[568,1404,732],{"className":1405},[731],[568,1407,1409],{"className":1408},[674],[568,1410,1412],{"className":1411,"style":739},[678],[568,1413],{},[568,1415],{"className":1416},[745,662]," und der Quotientenregel:",[568,1419,1422],{"className":1420},[1421],"katex-display",[568,1423,1425,1562],{"className":1424},[571],[568,1426,1428],{"className":1427},[575],[577,1429,1431],{"xmlns":579,"display":1430},"block",[581,1432,1433,1559],{},[584,1434,1435,1439,1441,1443,1445,1455,1457,1513,1515],{},[591,1436,1438],{"stretchy":1437},"false","(",[587,1440,1157],{},[591,1442,797],{},[587,1444,589],{},[788,1446,1447,1450],{},[591,1448,1449],{"stretchy":1437},")",[591,1451,1454],{"mathvariant":1452,"lspace":1453,"rspace":1453},"normal","0em","′",[591,1456,593],{},[595,1458,1459,1499],{},[584,1460,1461,1463,1465,1467,1470,1472,1474,1476,1479,1481,1483,1485,1487,1489,1491,1493,1495,1497],{},[587,1462,810],{},[591,1464,797],{},[587,1466,589],{},[591,1468,1469],{},"⋅",[587,1471,810],{},[591,1473,797],{},[587,1475,589],{},[591,1477,1478],{},"−",[587,1480,794],{},[591,1482,797],{},[587,1484,589],{},[591,1486,1469],{},[591,1488,1438],{"stretchy":1437},[591,1490,1478],{},[587,1492,794],{},[591,1494,797],{},[587,1496,589],{},[591,1498,1449],{"stretchy":1437},[584,1500,1501,1511],{},[788,1502,1503,1509],{},[584,1504,1505,1507],{},[587,1506,810],{},[591,1508,797],{},[601,1510,603],{},[587,1512,589],{},[591,1514,593],{},[595,1516,1517,1545],{},[584,1518,1519,1529,1531,1533,1543],{},[788,1520,1521,1527],{},[584,1522,1523,1525],{},[587,1524,810],{},[591,1526,797],{},[601,1528,603],{},[587,1530,589],{},[591,1532,606],{},[788,1534,1535,1541],{},[584,1536,1537,1539],{},[587,1538,794],{},[591,1540,797],{},[601,1542,603],{},[587,1544,589],{},[584,1546,1547,1557],{},[788,1548,1549,1555],{},[584,1550,1551,1553],{},[587,1552,810],{},[591,1554,797],{},[601,1556,603],{},[587,1558,589],{},[613,1560,1561],{"encoding":615},"(\\tan x)' = \\frac{\\cos x \\cdot \\cos x - \\sin x \\cdot (-\\sin x)}{\\cos^2 x} = \\frac{\\cos^2 x + \\sin^2 x}{\\cos^2 x}",[568,1563,1565,1627,1815],{"className":1564,"ariaHidden":621},[620],[568,1566,1568,1572,1575,1578,1581,1584,1618,1621,1624],{"className":1567},[625],[568,1569],{"className":1570,"style":1571},[629],"height:1.0519em;vertical-align:-0.25em;",[568,1573,1438],{"className":1574},[661],[568,1576,1157],{"className":1577},[838],[568,1579],{"className":1580,"style":872},[639],[568,1582,589],{"className":1583},[634,635],[568,1585,1587,1590],{"className":1586},[745],[568,1588,1449],{"className":1589},[745],[568,1591,1593],{"className":1592},[845],[568,1594,1596],{"className":1595},[669],[568,1597,1599],{"className":1598},[674],[568,1600,1603],{"className":1601,"style":1602},[678],"height:0.8019em;",[568,1604,1606,1609],{"style":1605},"top:-3.113em;margin-right:0.05em;",[568,1607],{"className":1608,"style":862},[686],[568,1610,1612],{"className":1611},[691,692,693,694],[568,1613,1615],{"className":1614},[634,694],[568,1616,1454],{"className":1617},[634,694],[568,1619],{"className":1620,"style":640},[639],[568,1622,593],{"className":1623},[644],[568,1625],{"className":1626,"style":640},[639],[568,1628,1630,1634,1806,1809,1812],{"className":1629},[625],[568,1631],{"className":1632,"style":1633},[629],"height:2.113em;vertical-align:-0.686em;",[568,1635,1637,1640,1803],{"className":1636},[634],[568,1638],{"className":1639},[661,662],[568,1641,1643],{"className":1642},[595],[568,1644,1646,1794],{"className":1645},[669,670],[568,1647,1649,1791],{"className":1648},[674],[568,1650,1653,1699,1707],{"className":1651,"style":1652},[678],"height:1.427em;",[568,1654,1656,1659],{"style":1655},"top:-2.314em;",[568,1657],{"className":1658,"style":687},[686],[568,1660,1662,1693,1696],{"className":1661},[634],[568,1663,1665,1668],{"className":1664},[838],[568,1666,810],{"className":1667},[838],[568,1669,1671],{"className":1670},[845],[568,1672,1674],{"className":1673},[669],[568,1675,1677],{"className":1676},[674],[568,1678,1681],{"className":1679,"style":1680},[678],"height:0.7401em;",[568,1682,1684,1687],{"style":1683},"top:-2.989em;margin-right:0.05em;",[568,1685],{"className":1686,"style":862},[686],[568,1688,1690],{"className":1689},[691,692,693,694],[568,1691,603],{"className":1692},[634,694],[568,1694],{"className":1695,"style":872},[639],[568,1697,589],{"className":1698},[634,635],[568,1700,1701,1704],{"style":703},[568,1702],{"className":1703,"style":687},[686],[568,1705],{"className":1706,"style":711},[710],[568,1708,1710,1713],{"style":1709},"top:-3.677em;",[568,1711],{"className":1712,"style":687},[686],[568,1714,1716,1719,1722,1725,1728,1731,1734,1737,1740,1743,1746,1749,1752,1755,1758,1761,1764,1767,1770,1773,1776,1779,1782,1785,1788],{"className":1715},[634],[568,1717,810],{"className":1718},[838],[568,1720],{"className":1721,"style":872},[639],[568,1723,589],{"className":1724},[634,635],[568,1726],{"className":1727,"style":749},[639],[568,1729,1469],{"className":1730},[753],[568,1732],{"className":1733,"style":749},[639],[568,1735,810],{"className":1736},[838],[568,1738],{"className":1739,"style":872},[639],[568,1741,589],{"className":1742},[634,635],[568,1744],{"className":1745,"style":749},[639],[568,1747,1478],{"className":1748},[753],[568,1750],{"className":1751,"style":749},[639],[568,1753,794],{"className":1754},[838],[568,1756],{"className":1757,"style":872},[639],[568,1759,589],{"className":1760},[634,635],[568,1762],{"className":1763,"style":749},[639],[568,1765,1469],{"className":1766},[753],[568,1768],{"className":1769,"style":749},[639],[568,1771,1438],{"className":1772},[661],[568,1774,1478],{"className":1775},[634],[568,1777],{"className":1778,"style":872},[639],[568,1780,794],{"className":1781},[838],[568,1783],{"className":1784,"style":872},[639],[568,1786,589],{"className":1787},[634,635],[568,1789,1449],{"className":1790},[745],[568,1792,732],{"className":1793},[731],[568,1795,1797],{"className":1796},[674],[568,1798,1801],{"className":1799,"style":1800},[678],"height:0.686em;",[568,1802],{},[568,1804],{"className":1805},[745,662],[568,1807],{"className":1808,"style":640},[639],[568,1810,593],{"className":1811},[644],[568,1813],{"className":1814,"style":640},[639],[568,1816,1818,1822],{"className":1817},[625],[568,1819],{"className":1820,"style":1821},[629],"height:2.2349em;vertical-align:-0.686em;",[568,1823,1825,1828,1990],{"className":1824},[634],[568,1826],{"className":1827},[661,662],[568,1829,1831],{"className":1830},[595],[568,1832,1834,1982],{"className":1833},[669,670],[568,1835,1837,1979],{"className":1836},[674],[568,1838,1841,1884,1892],{"className":1839,"style":1840},[678],"height:1.5489em;",[568,1842,1843,1846],{"style":1655},[568,1844],{"className":1845,"style":687},[686],[568,1847,1849,1878,1881],{"className":1848},[634],[568,1850,1852,1855],{"className":1851},[838],[568,1853,810],{"className":1854},[838],[568,1856,1858],{"className":1857},[845],[568,1859,1861],{"className":1860},[669],[568,1862,1864],{"className":1863},[674],[568,1865,1867],{"className":1866,"style":1680},[678],[568,1868,1869,1872],{"style":1683},[568,1870],{"className":1871,"style":862},[686],[568,1873,1875],{"className":1874},[691,692,693,694],[568,1876,603],{"className":1877},[634,694],[568,1879],{"className":1880,"style":872},[639],[568,1882,589],{"className":1883},[634,635],[568,1885,1886,1889],{"style":703},[568,1887],{"className":1888,"style":687},[686],[568,1890],{"className":1891,"style":711},[710],[568,1893,1894,1897],{"style":1709},[568,1895],{"className":1896,"style":687},[686],[568,1898,1900,1929,1932,1935,1938,1941,1944,1973,1976],{"className":1899},[634],[568,1901,1903,1906],{"className":1902},[838],[568,1904,810],{"className":1905},[838],[568,1907,1909],{"className":1908},[845],[568,1910,1912],{"className":1911},[669],[568,1913,1915],{"className":1914},[674],[568,1916,1918],{"className":1917,"style":891},[678],[568,1919,1920,1923],{"style":912},[568,1921],{"className":1922,"style":862},[686],[568,1924,1926],{"className":1925},[691,692,693,694],[568,1927,603],{"className":1928},[634,694],[568,1930],{"className":1931,"style":872},[639],[568,1933,589],{"className":1934},[634,635],[568,1936],{"className":1937,"style":749},[639],[568,1939,606],{"className":1940},[753],[568,1942],{"className":1943,"style":749},[639],[568,1945,1947,1950],{"className":1946},[838],[568,1948,794],{"className":1949},[838],[568,1951,1953],{"className":1952},[845],[568,1954,1956],{"className":1955},[669],[568,1957,1959],{"className":1958},[674],[568,1960,1962],{"className":1961,"style":855},[678],[568,1963,1964,1967],{"style":858},[568,1965],{"className":1966,"style":862},[686],[568,1968,1970],{"className":1969},[691,692,693,694],[568,1971,603],{"className":1972},[634,694],[568,1974],{"className":1975,"style":872},[639],[568,1977,589],{"className":1978},[634,635],[568,1980,732],{"className":1981},[731],[568,1983,1985],{"className":1984},[674],[568,1986,1988],{"className":1987,"style":1800},[678],[568,1989],{},[568,1991],{"className":1992},[745,662],[564,1994,1995,1996,2024,2025,2096,2097,2189],{},"Der Zähler ist ",[568,1997,1999,2012],{"className":1998},[571],[568,2000,2002],{"className":2001},[575],[577,2003,2004],{"xmlns":579},[581,2005,2006,2010],{},[584,2007,2008],{},[601,2009,821],{},[613,2011,821],{"encoding":615},[568,2013,2015],{"className":2014,"ariaHidden":621},[620],[568,2016,2018,2021],{"className":2017},[625],[568,2019],{"className":2020,"style":943},[629],[568,2022,821],{"className":2023},[634],". Teilt man stattdessen jeden Summanden einzeln durch ",[568,2026,2028,2052],{"className":2027},[571],[568,2029,2031],{"className":2030},[575],[577,2032,2033],{"xmlns":579},[581,2034,2035,2049],{},[584,2036,2037,2047],{},[788,2038,2039,2045],{},[584,2040,2041,2043],{},[587,2042,810],{},[591,2044,797],{},[601,2046,603],{},[587,2048,589],{},[613,2050,2051],{"encoding":615},"\\cos^2 x",[568,2053,2055],{"className":2054,"ariaHidden":621},[620],[568,2056,2058,2061,2090,2093],{"className":2057},[625],[568,2059],{"className":2060,"style":891},[629],[568,2062,2064,2067],{"className":2063},[838],[568,2065,810],{"className":2066},[838],[568,2068,2070],{"className":2069},[845],[568,2071,2073],{"className":2072},[669],[568,2074,2076],{"className":2075},[674],[568,2077,2079],{"className":2078,"style":891},[678],[568,2080,2081,2084],{"style":912},[568,2082],{"className":2083,"style":862},[686],[568,2085,2087],{"className":2086},[691,692,693,694],[568,2088,603],{"className":2089},[634,694],[568,2091],{"className":2092,"style":872},[639],[568,2094,589],{"className":2095},[634,635],", erhält man ",[568,2098,2100,2127],{"className":2099},[571],[568,2101,2103],{"className":2102},[575],[577,2104,2105],{"xmlns":579},[581,2106,2107,2125],{},[584,2108,2109,2111,2113,2123],{},[601,2110,821],{},[591,2112,606],{},[788,2114,2115,2121],{},[584,2116,2117,2119],{},[587,2118,1157],{},[591,2120,797],{},[601,2122,603],{},[587,2124,589],{},[613,2126,1166],{"encoding":615},[568,2128,2130,2148],{"className":2129,"ariaHidden":621},[620],[568,2131,2133,2136,2139,2142,2145],{"className":2132},[625],[568,2134],{"className":2135,"style":1176},[629],[568,2137,821],{"className":2138},[634],[568,2140],{"className":2141,"style":749},[639],[568,2143,606],{"className":2144},[753],[568,2146],{"className":2147,"style":749},[639],[568,2149,2151,2154,2183,2186],{"className":2150},[625],[568,2152],{"className":2153,"style":1195},[629],[568,2155,2157,2160],{"className":2156},[838],[568,2158,1157],{"className":2159},[838],[568,2161,2163],{"className":2162},[845],[568,2164,2166],{"className":2165},[669],[568,2167,2169],{"className":2168},[674],[568,2170,2172],{"className":2171,"style":1195},[678],[568,2173,2174,2177],{"style":1216},[568,2175],{"className":2176,"style":862},[686],[568,2178,2180],{"className":2179},[691,692,693,694],[568,2181,603],{"className":2182},[634,694],[568,2184],{"className":2185,"style":872},[639],[568,2187,589],{"className":2188},[634,635],".",[559,2191,2193],{"id":2192},"beispiele","Beispiele",[564,2195,2196,2197,2318,2319,2481,2482,2543],{},"An der Stelle ",[568,2198,2200,2223],{"className":2199},[571],[568,2201,2203],{"className":2202},[575],[577,2204,2205],{"xmlns":579},[581,2206,2207,2220],{},[584,2208,2209,2211,2213],{},[587,2210,589],{},[591,2212,593],{},[595,2214,2215,2217],{},[587,2216,599],{},[601,2218,2219],{},"4",[613,2221,2222],{"encoding":615},"x = \\frac{\\pi}{4}",[568,2224,2226,2244],{"className":2225,"ariaHidden":621},[620],[568,2227,2229,2232,2235,2238,2241],{"className":2228},[625],[568,2230],{"className":2231,"style":630},[629],[568,2233,589],{"className":2234},[634,635],[568,2236],{"className":2237,"style":640},[639],[568,2239,593],{"className":2240},[644],[568,2242],{"className":2243,"style":640},[639],[568,2245,2247,2250],{"className":2246},[625],[568,2248],{"className":2249,"style":654},[629],[568,2251,2253,2256,2315],{"className":2252},[634],[568,2254],{"className":2255},[661,662],[568,2257,2259],{"className":2258},[595],[568,2260,2262,2307],{"className":2261},[669,670],[568,2263,2265,2304],{"className":2264},[674],[568,2266,2268,2282,2290],{"className":2267,"style":679},[678],[568,2269,2270,2273],{"style":682},[568,2271],{"className":2272,"style":687},[686],[568,2274,2276],{"className":2275},[691,692,693,694],[568,2277,2279],{"className":2278},[634,694],[568,2280,2219],{"className":2281},[634,694],[568,2283,2284,2287],{"style":703},[568,2285],{"className":2286,"style":687},[686],[568,2288],{"className":2289,"style":711},[710],[568,2291,2292,2295],{"style":714},[568,2293],{"className":2294,"style":687},[686],[568,2296,2298],{"className":2297},[691,692,693,694],[568,2299,2301],{"className":2300},[634,694],[568,2302,599],{"className":2303,"style":727},[634,635,694],[568,2305,732],{"className":2306},[731],[568,2308,2310],{"className":2309},[674],[568,2311,2313],{"className":2312,"style":739},[678],[568,2314],{},[568,2316],{"className":2317},[745,662]," ist ",[568,2320,2322,2354],{"className":2321},[571],[568,2323,2325],{"className":2324},[575],[577,2326,2327],{"xmlns":579},[581,2328,2329,2351],{},[584,2330,2331,2341,2343,2345],{},[788,2332,2333,2339],{},[584,2334,2335,2337],{},[587,2336,810],{},[591,2338,797],{},[601,2340,603],{},[587,2342,589],{},[591,2344,593],{},[595,2346,2347,2349],{},[601,2348,821],{},[601,2350,603],{},[613,2352,2353],{"encoding":615},"\\cos^2 x = \\frac{1}{2}",[568,2355,2357,2407],{"className":2356,"ariaHidden":621},[620],[568,2358,2360,2363,2392,2395,2398,2401,2404],{"className":2359},[625],[568,2361],{"className":2362,"style":891},[629],[568,2364,2366,2369],{"className":2365},[838],[568,2367,810],{"className":2368},[838],[568,2370,2372],{"className":2371},[845],[568,2373,2375],{"className":2374},[669],[568,2376,2378],{"className":2377},[674],[568,2379,2381],{"className":2380,"style":891},[678],[568,2382,2383,2386],{"style":912},[568,2384],{"className":2385,"style":862},[686],[568,2387,2389],{"className":2388},[691,692,693,694],[568,2390,603],{"className":2391},[634,694],[568,2393],{"className":2394,"style":872},[639],[568,2396,589],{"className":2397},[634,635],[568,2399],{"className":2400,"style":640},[639],[568,2402,593],{"className":2403},[644],[568,2405],{"className":2406,"style":640},[639],[568,2408,2410,2413],{"className":2409},[625],[568,2411],{"className":2412,"style":996},[629],[568,2414,2416,2419,2478],{"className":2415},[634],[568,2417],{"className":2418},[661,662],[568,2420,2422],{"className":2421},[595],[568,2423,2425,2470],{"className":2424},[669,670],[568,2426,2428,2467],{"className":2427},[674],[568,2429,2431,2445,2453],{"className":2430,"style":1015},[678],[568,2432,2433,2436],{"style":682},[568,2434],{"className":2435,"style":687},[686],[568,2437,2439],{"className":2438},[691,692,693,694],[568,2440,2442],{"className":2441},[634,694],[568,2443,603],{"className":2444},[634,694],[568,2446,2447,2450],{"style":703},[568,2448],{"className":2449,"style":687},[686],[568,2451],{"className":2452,"style":711},[710],[568,2454,2455,2458],{"style":714},[568,2456],{"className":2457,"style":687},[686],[568,2459,2461],{"className":2460},[691,692,693,694],[568,2462,2464],{"className":2463},[634,694],[568,2465,821],{"className":2466},[634,694],[568,2468,732],{"className":2469},[731],[568,2471,2473],{"className":2472},[674],[568,2474,2476],{"className":2475,"style":739},[678],[568,2477],{},[568,2479],{"className":2480},[745,662]," und ",[568,2483,2485,2507],{"className":2484},[571],[568,2486,2488],{"className":2487},[575],[577,2489,2490],{"xmlns":579},[581,2491,2492,2504],{},[584,2493,2494,2496,2498,2500,2502],{},[587,2495,1157],{},[591,2497,797],{},[587,2499,589],{},[591,2501,593],{},[601,2503,821],{},[613,2505,2506],{"encoding":615},"\\tan x = 1",[568,2508,2510,2534],{"className":2509,"ariaHidden":621},[620],[568,2511,2513,2516,2519,2522,2525,2528,2531],{"className":2512},[625],[568,2514],{"className":2515,"style":1290},[629],[568,2517,1157],{"className":2518},[838],[568,2520],{"className":2521,"style":872},[639],[568,2523,589],{"className":2524},[634,635],[568,2526],{"className":2527,"style":640},[639],[568,2529,593],{"className":2530},[644],[568,2532],{"className":2533,"style":640},[639],[568,2535,2537,2540],{"className":2536},[625],[568,2538],{"className":2539,"style":943},[629],[568,2541,821],{"className":2542},[634],":",[568,2545,2547],{"className":2546},[1421],[568,2548,2550,2613],{"className":2549},[571],[568,2551,2553],{"className":2552},[575],[577,2554,2555],{"xmlns":579,"display":1430},[581,2556,2557,2610],{},[584,2558,2559,2566,2570,2582,2584,2594,2596,2598,2600,2602,2604],{},[788,2560,2561,2564],{},[587,2562,2563],{},"f",[591,2565,1454],{"mathvariant":1452,"lspace":1453,"rspace":1453},[2567,2568,2569],"mtext",{}," ⁣",[584,2571,2572,2574,2580],{},[591,2573,1438],{"fence":621},[595,2575,2576,2578],{},[587,2577,599],{},[601,2579,2219],{},[591,2581,1449],{"fence":621},[591,2583,593],{},[595,2585,2586,2588],{},[601,2587,821],{},[595,2589,2590,2592],{},[601,2591,821],{},[601,2593,603],{},[591,2595,593],{},[601,2597,603],{},[591,2599,593],{},[601,2601,821],{},[591,2603,606],{},[788,2605,2606,2608],{},[601,2607,821],{},[601,2609,603],{},[613,2611,2612],{"encoding":615},"f'\\!\\left(\\frac{\\pi}{4}\\right) = \\frac{1}{\\frac{1}{2}} = 2 = 1 + 1^2",[568,2614,2616,2755,2901,2919,2937],{"className":2615,"ariaHidden":621},[620],[568,2617,2619,2623,2656,2660,2663,2746,2749,2752],{"className":2618},[625],[568,2620],{"className":2621,"style":2622},[629],"height:1.836em;vertical-align:-0.686em;",[568,2624,2626,2630],{"className":2625},[634],[568,2627,2563],{"className":2628,"style":2629},[634,635],"margin-right:0.1076em;",[568,2631,2633],{"className":2632},[845],[568,2634,2636],{"className":2635},[669],[568,2637,2639],{"className":2638},[674],[568,2640,2642],{"className":2641,"style":1602},[678],[568,2643,2644,2647],{"style":1605},[568,2645],{"className":2646,"style":862},[686],[568,2648,2650],{"className":2649},[691,692,693,694],[568,2651,2653],{"className":2652},[634,694],[568,2654,1454],{"className":2655},[634,694],[568,2657],{"className":2658,"style":2659},[639],"margin-right:-0.1667em;",[568,2661],{"className":2662,"style":872},[639],[568,2664,2667,2677,2740],{"className":2665},[2666],"minner",[568,2668,2672],{"className":2669,"style":2671},[661,2670],"delimcenter","top:0em;",[568,2673,1438],{"className":2674},[2675,2676],"delimsizing","size2",[568,2678,2680,2683,2737],{"className":2679},[634],[568,2681],{"className":2682},[661,662],[568,2684,2686],{"className":2685},[595],[568,2687,2689,2729],{"className":2688},[669,670],[568,2690,2692,2726],{"className":2691},[674],[568,2693,2696,2707,2715],{"className":2694,"style":2695},[678],"height:1.1076em;",[568,2697,2698,2701],{"style":1655},[568,2699],{"className":2700,"style":687},[686],[568,2702,2704],{"className":2703},[634],[568,2705,2219],{"className":2706},[634],[568,2708,2709,2712],{"style":703},[568,2710],{"className":2711,"style":687},[686],[568,2713],{"className":2714,"style":711},[710],[568,2716,2717,2720],{"style":1709},[568,2718],{"className":2719,"style":687},[686],[568,2721,2723],{"className":2722},[634],[568,2724,599],{"className":2725,"style":727},[634,635],[568,2727,732],{"className":2728},[731],[568,2730,2732],{"className":2731},[674],[568,2733,2735],{"className":2734,"style":1800},[678],[568,2736],{},[568,2738],{"className":2739},[745,662],[568,2741,2743],{"className":2742,"style":2671},[745,2670],[568,2744,1449],{"className":2745},[2675,2676],[568,2747],{"className":2748,"style":640},[639],[568,2750,593],{"className":2751},[644],[568,2753],{"className":2754,"style":640},[639],[568,2756,2758,2762,2892,2895,2898],{"className":2757},[625],[568,2759],{"className":2760,"style":2761},[629],"height:2.4015em;vertical-align:-1.0801em;",[568,2763,2765,2768,2889],{"className":2764},[634],[568,2766],{"className":2767},[661,662],[568,2769,2771],{"className":2770},[595],[568,2772,2774,2880],{"className":2773},[669,670],[568,2775,2777,2877],{"className":2776},[674],[568,2778,2781,2858,2866],{"className":2779,"style":2780},[678],"height:1.3214em;",[568,2782,2784,2787],{"style":2783},"top:-2.2649em;",[568,2785],{"className":2786,"style":687},[686],[568,2788,2790],{"className":2789},[634],[568,2791,2793,2796,2855],{"className":2792},[634],[568,2794],{"className":2795},[661,662],[568,2797,2799],{"className":2798},[595],[568,2800,2802,2847],{"className":2801},[669,670],[568,2803,2805,2844],{"className":2804},[674],[568,2806,2808,2822,2830],{"className":2807,"style":1015},[678],[568,2809,2810,2813],{"style":682},[568,2811],{"className":2812,"style":687},[686],[568,2814,2816],{"className":2815},[691,692,693,694],[568,2817,2819],{"className":2818},[634,694],[568,2820,603],{"className":2821},[634,694],[568,2823,2824,2827],{"style":703},[568,2825],{"className":2826,"style":687},[686],[568,2828],{"className":2829,"style":711},[710],[568,2831,2832,2835],{"style":714},[568,2833],{"className":2834,"style":687},[686],[568,2836,2838],{"className":2837},[691,692,693,694],[568,2839,2841],{"className":2840},[634,694],[568,2842,821],{"className":2843},[634,694],[568,2845,732],{"className":2846},[731],[568,2848,2850],{"className":2849},[674],[568,2851,2853],{"className":2852,"style":739},[678],[568,2854],{},[568,2856],{"className":2857},[745,662],[568,2859,2860,2863],{"style":703},[568,2861],{"className":2862,"style":687},[686],[568,2864],{"className":2865,"style":711},[710],[568,2867,2868,2871],{"style":1709},[568,2869],{"className":2870,"style":687},[686],[568,2872,2874],{"className":2873},[634],[568,2875,821],{"className":2876},[634],[568,2878,732],{"className":2879},[731],[568,2881,2883],{"className":2882},[674],[568,2884,2887],{"className":2885,"style":2886},[678],"height:1.0801em;",[568,2888],{},[568,2890],{"className":2891},[745,662],[568,2893],{"className":2894,"style":640},[639],[568,2896,593],{"className":2897},[644],[568,2899],{"className":2900,"style":640},[639],[568,2902,2904,2907,2910,2913,2916],{"className":2903},[625],[568,2905],{"className":2906,"style":943},[629],[568,2908,603],{"className":2909},[634],[568,2911],{"className":2912,"style":640},[639],[568,2914,593],{"className":2915},[644],[568,2917],{"className":2918,"style":640},[639],[568,2920,2922,2925,2928,2931,2934],{"className":2921},[625],[568,2923],{"className":2924,"style":1176},[629],[568,2926,821],{"className":2927},[634],[568,2929],{"className":2930,"style":749},[639],[568,2932,606],{"className":2933},[753],[568,2935],{"className":2936,"style":749},[639],[568,2938,2940,2944],{"className":2939},[625],[568,2941],{"className":2942,"style":2943},[629],"height:0.8641em;",[568,2945,2947,2950],{"className":2946},[634],[568,2948,821],{"className":2949},[634],[568,2951,2953],{"className":2952},[845],[568,2954,2956],{"className":2955},[669],[568,2957,2959],{"className":2958},[674],[568,2960,2962],{"className":2961,"style":2943},[678],[568,2963,2964,2967],{"style":1605},[568,2965],{"className":2966,"style":862},[686],[568,2968,2970],{"className":2969},[691,692,693,694],[568,2971,603],{"className":2972},[634,694],[564,2974,2975],{},"Mit der Kettenregel:",[568,2977,2979],{"className":2978},[1421],[568,2980,2982,3063],{"className":2981},[571],[568,2983,2985],{"className":2984},[575],[577,2986,2987],{"xmlns":579,"display":1430},[581,2988,2989,3060],{},[584,2990,2991,2993,2995,2997,2999,3001,3003,3005,3007,3010,3012,3014,3017,3020,3022,3028,3030,3032,3034,3036],{},[587,2992,2563],{},[591,2994,1438],{"stretchy":1437},[587,2996,589],{},[591,2998,1449],{"stretchy":1437},[591,3000,593],{},[587,3002,1157],{},[591,3004,797],{},[591,3006,1438],{"stretchy":1437},[601,3008,3009],{},"3",[587,3011,589],{},[591,3013,1449],{"stretchy":1437},[2567,3015,3016],{},"  ",[591,3018,3019],{},"⇒",[2567,3021,3016],{},[788,3023,3024,3026],{},[587,3025,2563],{},[591,3027,1454],{"mathvariant":1452,"lspace":1453,"rspace":1453},[591,3029,1438],{"stretchy":1437},[587,3031,589],{},[591,3033,1449],{"stretchy":1437},[591,3035,593],{},[595,3037,3038,3040],{},[601,3039,3009],{},[584,3041,3042,3052,3054,3056,3058],{},[788,3043,3044,3050],{},[584,3045,3046,3048],{},[587,3047,810],{},[591,3049,797],{},[601,3051,603],{},[591,3053,1438],{"stretchy":1437},[601,3055,3009],{},[587,3057,589],{},[591,3059,1449],{"stretchy":1437},[613,3061,3062],{"encoding":615},"f(x) = \\tan(3x) \\;\\Rightarrow\\; f'(x) = \\frac{3}{\\cos^2(3x)}",[568,3064,3066,3094,3130,3186],{"className":3065,"ariaHidden":621},[620],[568,3067,3069,3073,3076,3079,3082,3085,3088,3091],{"className":3068},[625],[568,3070],{"className":3071,"style":3072},[629],"height:1em;vertical-align:-0.25em;",[568,3074,2563],{"className":3075,"style":2629},[634,635],[568,3077,1438],{"className":3078},[661],[568,3080,589],{"className":3081},[634,635],[568,3083,1449],{"className":3084},[745],[568,3086],{"className":3087,"style":640},[639],[568,3089,593],{"className":3090},[644],[568,3092],{"className":3093,"style":640},[639],[568,3095,3097,3100,3103,3106,3109,3112,3115,3118,3121,3124,3127],{"className":3096},[625],[568,3098],{"className":3099,"style":3072},[629],[568,3101,1157],{"className":3102},[838],[568,3104,1438],{"className":3105},[661],[568,3107,3009],{"className":3108},[634],[568,3110,589],{"className":3111},[634,635],[568,3113,1449],{"className":3114},[745],[568,3116],{"className":3117,"style":640},[639],[568,3119],{"className":3120,"style":640},[639],[568,3122,3019],{"className":3123},[644],[568,3125],{"className":3126,"style":640},[639],[568,3128],{"className":3129,"style":640},[639],[568,3131,3133,3136,3168,3171,3174,3177,3180,3183],{"className":3132},[625],[568,3134],{"className":3135,"style":1571},[629],[568,3137,3139,3142],{"className":3138},[634],[568,3140,2563],{"className":3141,"style":2629},[634,635],[568,3143,3145],{"className":3144},[845],[568,3146,3148],{"className":3147},[669],[568,3149,3151],{"className":3150},[674],[568,3152,3154],{"className":3153,"style":1602},[678],[568,3155,3156,3159],{"style":1605},[568,3157],{"className":3158,"style":862},[686],[568,3160,3162],{"className":3161},[691,692,693,694],[568,3163,3165],{"className":3164},[634,694],[568,3166,1454],{"className":3167},[634,694],[568,3169,1438],{"className":3170},[661],[568,3172,589],{"className":3173},[634,635],[568,3175,1449],{"className":3176},[745],[568,3178],{"className":3179,"style":640},[639],[568,3181,593],{"className":3182},[644],[568,3184],{"className":3185,"style":640},[639],[568,3187,3189,3193],{"className":3188},[625],[568,3190],{"className":3191,"style":3192},[629],"height:2.2574em;vertical-align:-0.936em;",[568,3194,3196,3199,3291],{"className":3195},[634],[568,3197],{"className":3198},[661,662],[568,3200,3202],{"className":3201},[595],[568,3203,3205,3282],{"className":3204},[669,670],[568,3206,3208,3279],{"className":3207},[674],[568,3209,3211,3260,3268],{"className":3210,"style":2780},[678],[568,3212,3213,3216],{"style":1655},[568,3214],{"className":3215,"style":687},[686],[568,3217,3219,3248,3251,3254,3257],{"className":3218},[634],[568,3220,3222,3225],{"className":3221},[838],[568,3223,810],{"className":3224},[838],[568,3226,3228],{"className":3227},[845],[568,3229,3231],{"className":3230},[669],[568,3232,3234],{"className":3233},[674],[568,3235,3237],{"className":3236,"style":1680},[678],[568,3238,3239,3242],{"style":1683},[568,3240],{"className":3241,"style":862},[686],[568,3243,3245],{"className":3244},[691,692,693,694],[568,3246,603],{"className":3247},[634,694],[568,3249,1438],{"className":3250},[661],[568,3252,3009],{"className":3253},[634],[568,3255,589],{"className":3256},[634,635],[568,3258,1449],{"className":3259},[745],[568,3261,3262,3265],{"style":703},[568,3263],{"className":3264,"style":687},[686],[568,3266],{"className":3267,"style":711},[710],[568,3269,3270,3273],{"style":1709},[568,3271],{"className":3272,"style":687},[686],[568,3274,3276],{"className":3275},[634],[568,3277,3009],{"className":3278},[634],[568,3280,732],{"className":3281},[731],[568,3283,3285],{"className":3284},[674],[568,3286,3289],{"className":3287,"style":3288},[678],"height:0.936em;",[568,3290],{},[568,3292],{"className":3293},[745,662],[559,3295,3297],{"id":3296},"typische-fehler","Typische Fehler",[3299,3300,3301,3606,3900],"ul",{},[3302,3303,3304,3455,3456,3605],"li",{},[568,3305,3307,3337],{"className":3306},[571],[568,3308,3310],{"className":3309},[575],[577,3311,3312],{"xmlns":579},[581,3313,3314,3334],{},[584,3315,3316],{},[595,3317,3318,3320],{},[601,3319,821],{},[584,3321,3322,3332],{},[788,3323,3324,3330],{},[584,3325,3326,3328],{},[587,3327,810],{},[591,3329,797],{},[601,3331,603],{},[587,3333,589],{},[613,3335,3336],{"encoding":615},"\\frac{1}{\\cos^2 x}",[568,3338,3340],{"className":3339,"ariaHidden":621},[620],[568,3341,3343,3346],{"className":3342},[625],[568,3344],{"className":3345,"style":996},[629],[568,3347,3349,3352,3452],{"className":3348},[634],[568,3350],{"className":3351},[661,662],[568,3353,3355],{"className":3354},[595],[568,3356,3358,3444],{"className":3357},[669,670],[568,3359,3361,3441],{"className":3360},[674],[568,3362,3364,3419,3427],{"className":3363,"style":1015},[678],[568,3365,3366,3369],{"style":682},[568,3367],{"className":3368,"style":687},[686],[568,3370,3372],{"className":3371},[691,692,693,694],[568,3373,3375,3413,3416],{"className":3374},[634,694],[568,3376,3378,3390],{"className":3377},[838,694],[568,3379,3381,3384,3387],{"className":3380},[838,694],[568,3382,1036],{"className":3383},[694],[568,3385,1040],{"className":3386},[694],[568,3388,1044],{"className":3389},[694],[568,3391,3393],{"className":3392},[845],[568,3394,3396],{"className":3395},[669],[568,3397,3399],{"className":3398},[674],[568,3400,3402],{"className":3401,"style":1057},[678],[568,3403,3404,3407],{"style":1060},[568,3405],{"className":3406,"style":1064},[686],[568,3408,3410],{"className":3409},[691,1068,1069,694],[568,3411,603],{"className":3412},[634,694],[568,3414],{"className":3415,"style":1076},[639,694],[568,3417,589],{"className":3418},[634,635,694],[568,3420,3421,3424],{"style":703},[568,3422],{"className":3423,"style":687},[686],[568,3425],{"className":3426,"style":711},[710],[568,3428,3429,3432],{"style":714},[568,3430],{"className":3431,"style":687},[686],[568,3433,3435],{"className":3434},[691,692,693,694],[568,3436,3438],{"className":3437},[634,694],[568,3439,821],{"className":3440},[634,694],[568,3442,732],{"className":3443},[731],[568,3445,3447],{"className":3446},[674],[568,3448,3450],{"className":3449,"style":739},[678],[568,3451],{},[568,3453],{"className":3454},[745,662]," mit ",[568,3457,3459,3487],{"className":3458},[571],[568,3460,3462],{"className":3461},[575],[577,3463,3464],{"xmlns":579},[581,3465,3466,3484],{},[584,3467,3468],{},[595,3469,3470,3472],{},[601,3471,821],{},[584,3473,3474,3476,3478],{},[587,3475,810],{},[591,3477,797],{},[788,3479,3480,3482],{},[587,3481,589],{},[601,3483,603],{},[613,3485,3486],{"encoding":615},"\\frac{1}{\\cos x^2}",[568,3488,3490],{"className":3489,"ariaHidden":621},[620],[568,3491,3493,3496],{"className":3492},[625],[568,3494],{"className":3495,"style":996},[629],[568,3497,3499,3502,3602],{"className":3498},[634],[568,3500],{"className":3501},[661,662],[568,3503,3505],{"className":3504},[595],[568,3506,3508,3594],{"className":3507},[669,670],[568,3509,3511,3591],{"className":3510},[674],[568,3512,3514,3569,3577],{"className":3513,"style":1015},[678],[568,3515,3516,3519],{"style":682},[568,3517],{"className":3518,"style":687},[686],[568,3520,3522],{"className":3521},[691,692,693,694],[568,3523,3525,3537,3540],{"className":3524},[634,694],[568,3526,3528,3531,3534],{"className":3527},[838,694],[568,3529,1036],{"className":3530},[694],[568,3532,1040],{"className":3533},[694],[568,3535,1044],{"className":3536},[694],[568,3538],{"className":3539,"style":1076},[639,694],[568,3541,3543,3546],{"className":3542},[634,694],[568,3544,589],{"className":3545},[634,635,694],[568,3547,3549],{"className":3548},[845],[568,3550,3552],{"className":3551},[669],[568,3553,3555],{"className":3554},[674],[568,3556,3558],{"className":3557,"style":1057},[678],[568,3559,3560,3563],{"style":1060},[568,3561],{"className":3562,"style":1064},[686],[568,3564,3566],{"className":3565},[691,1068,1069,694],[568,3567,603],{"className":3568},[634,694],[568,3570,3571,3574],{"style":703},[568,3572],{"className":3573,"style":687},[686],[568,3575],{"className":3576,"style":711},[710],[568,3578,3579,3582],{"style":714},[568,3580],{"className":3581,"style":687},[686],[568,3583,3585],{"className":3584},[691,692,693,694],[568,3586,3588],{"className":3587},[634,694],[568,3589,821],{"className":3590},[634,694],[568,3592,732],{"className":3593},[731],[568,3595,3597],{"className":3596},[674],[568,3598,3600],{"className":3599,"style":739},[678],[568,3601],{},[568,3603],{"className":3604},[745,662]," verwechseln. Quadriert wird der Funktionswert, nicht das Argument.",[3302,3607,3608,3609,3734,3735,3871,3872,2189],{},"In der Quotientenregel das Minus von ",[568,3610,3612,3648],{"className":3611},[571],[568,3613,3615],{"className":3614},[575],[577,3616,3617],{"xmlns":579},[581,3618,3619,3645],{},[584,3620,3621,3623,3625,3627,3629,3635,3637,3639,3641,3643],{},[591,3622,1438],{"stretchy":1437},[587,3624,810],{},[591,3626,797],{},[587,3628,589],{},[788,3630,3631,3633],{},[591,3632,1449],{"stretchy":1437},[591,3634,1454],{"mathvariant":1452,"lspace":1453,"rspace":1453},[591,3636,593],{},[591,3638,1478],{},[587,3640,794],{},[591,3642,797],{},[587,3644,589],{},[613,3646,3647],{"encoding":615},"(\\cos x)' = -\\sin x",[568,3649,3651,3712],{"className":3650,"ariaHidden":621},[620],[568,3652,3654,3658,3661,3664,3667,3670,3703,3706,3709],{"className":3653},[625],[568,3655],{"className":3656,"style":3657},[629],"height:1.0019em;vertical-align:-0.25em;",[568,3659,1438],{"className":3660},[661],[568,3662,810],{"className":3663},[838],[568,3665],{"className":3666,"style":872},[639],[568,3668,589],{"className":3669},[634,635],[568,3671,3673,3676],{"className":3672},[745],[568,3674,1449],{"className":3675},[745],[568,3677,3679],{"className":3678},[845],[568,3680,3682],{"className":3681},[669],[568,3683,3685],{"className":3684},[674],[568,3686,3689],{"className":3687,"style":3688},[678],"height:0.7519em;",[568,3690,3691,3694],{"style":912},[568,3692],{"className":3693,"style":862},[686],[568,3695,3697],{"className":3696},[691,692,693,694],[568,3698,3700],{"className":3699},[634,694],[568,3701,1454],{"className":3702},[634,694],[568,3704],{"className":3705,"style":640},[639],[568,3707,593],{"className":3708},[644],[568,3710],{"className":3711,"style":640},[639],[568,3713,3715,3719,3722,3725,3728,3731],{"className":3714},[625],[568,3716],{"className":3717,"style":3718},[629],"height:0.7512em;vertical-align:-0.0833em;",[568,3720,1478],{"className":3721},[634],[568,3723],{"className":3724,"style":872},[639],[568,3726,794],{"className":3727},[838],[568,3729],{"className":3730,"style":872},[639],[568,3732,589],{"className":3733},[634,635]," verlieren. Dann steht im Zähler ",[568,3736,3738,3776],{"className":3737},[571],[568,3739,3741],{"className":3740},[575],[577,3742,3743],{"xmlns":579},[581,3744,3745,3773],{},[584,3746,3747,3757,3759,3761,3771],{},[788,3748,3749,3755],{},[584,3750,3751,3753],{},[587,3752,810],{},[591,3754,797],{},[601,3756,603],{},[587,3758,589],{},[591,3760,1478],{},[788,3762,3763,3769],{},[584,3764,3765,3767],{},[587,3766,794],{},[591,3768,797],{},[601,3770,603],{},[587,3772,589],{},[613,3774,3775],{"encoding":615},"\\cos^2 x - \\sin^2 x",[568,3777,3779,3830],{"className":3778,"ariaHidden":621},[620],[568,3780,3782,3786,3815,3818,3821,3824,3827],{"className":3781},[625],[568,3783],{"className":3784,"style":3785},[629],"height:0.8974em;vertical-align:-0.0833em;",[568,3787,3789,3792],{"className":3788},[838],[568,3790,810],{"className":3791},[838],[568,3793,3795],{"className":3794},[845],[568,3796,3798],{"className":3797},[669],[568,3799,3801],{"className":3800},[674],[568,3802,3804],{"className":3803,"style":891},[678],[568,3805,3806,3809],{"style":912},[568,3807],{"className":3808,"style":862},[686],[568,3810,3812],{"className":3811},[691,692,693,694],[568,3813,603],{"className":3814},[634,694],[568,3816],{"className":3817,"style":872},[639],[568,3819,589],{"className":3820},[634,635],[568,3822],{"className":3823,"style":749},[639],[568,3825,1478],{"className":3826},[753],[568,3828],{"className":3829,"style":749},[639],[568,3831,3833,3836,3865,3868],{"className":3832},[625],[568,3834],{"className":3835,"style":855},[629],[568,3837,3839,3842],{"className":3838},[838],[568,3840,794],{"className":3841},[838],[568,3843,3845],{"className":3844},[845],[568,3846,3848],{"className":3847},[669],[568,3849,3851],{"className":3850},[674],[568,3852,3854],{"className":3853,"style":855},[678],[568,3855,3856,3859],{"style":858},[568,3857],{"className":3858,"style":862},[686],[568,3860,3862],{"className":3861},[691,692,693,694],[568,3863,603],{"className":3864},[634,694],[568,3866],{"className":3867,"style":872},[639],[568,3869,589],{"className":3870},[634,635]," statt ",[568,3873,3875,3888],{"className":3874},[571],[568,3876,3878],{"className":3877},[575],[577,3879,3880],{"xmlns":579},[581,3881,3882,3886],{},[584,3883,3884],{},[601,3885,821],{},[613,3887,821],{"encoding":615},[568,3889,3891],{"className":3890,"ariaHidden":621},[620],[568,3892,3894,3897],{"className":3893},[625],[568,3895],{"className":3896,"style":943},[629],[568,3898,821],{"className":3899},[634],[3302,3901,3902,3903,2189],{},"Die Ableitung an Polstellen auswerten, z.B. bei ",[568,3904,3906,3928],{"className":3905},[571],[568,3907,3909],{"className":3908},[575],[577,3910,3911],{"xmlns":579},[581,3912,3913,3925],{},[584,3914,3915,3917,3919],{},[587,3916,589],{},[591,3918,593],{},[595,3920,3921,3923],{},[587,3922,599],{},[601,3924,603],{},[613,3926,3927],{"encoding":615},"x = \\frac{\\pi}{2}",[568,3929,3931,3949],{"className":3930,"ariaHidden":621},[620],[568,3932,3934,3937,3940,3943,3946],{"className":3933},[625],[568,3935],{"className":3936,"style":630},[629],[568,3938,589],{"className":3939},[634,635],[568,3941],{"className":3942,"style":640},[639],[568,3944,593],{"className":3945},[644],[568,3947],{"className":3948,"style":640},[639],[568,3950,3952,3955],{"className":3951},[625],[568,3953],{"className":3954,"style":654},[629],[568,3956,3958,3961,4020],{"className":3957},[634],[568,3959],{"className":3960},[661,662],[568,3962,3964],{"className":3963},[595],[568,3965,3967,4012],{"className":3966},[669,670],[568,3968,3970,4009],{"className":3969},[674],[568,3971,3973,3987,3995],{"className":3972,"style":679},[678],[568,3974,3975,3978],{"style":682},[568,3976],{"className":3977,"style":687},[686],[568,3979,3981],{"className":3980},[691,692,693,694],[568,3982,3984],{"className":3983},[634,694],[568,3985,603],{"className":3986},[634,694],[568,3988,3989,3992],{"style":703},[568,3990],{"className":3991,"style":687},[686],[568,3993],{"className":3994,"style":711},[710],[568,3996,3997,4000],{"style":714},[568,3998],{"className":3999,"style":687},[686],[568,4001,4003],{"className":4002},[691,692,693,694],[568,4004,4006],{"className":4005},[634,694],[568,4007,599],{"className":4008,"style":727},[634,635,694],[568,4010,732],{"className":4011},[731],[568,4013,4015],{"className":4014},[674],[568,4016,4018],{"className":4017,"style":739},[678],[568,4019],{},[568,4021],{"className":4022},[745,662],{"title":4024,"searchDepth":4025,"depth":4025,"links":4026},"",2,[4027,4028,4029,4030],{"id":561,"depth":4025,"text":562},{"id":1235,"depth":4025,"text":1236},{"id":2192,"depth":4025,"text":2193},{"id":3296,"depth":4025,"text":3297},[4032,4035,4037,4041,4044,4046,4048],{"lhs":4033,"rhs":4034},"1\u002Fcos(x)^2","1 + tan(x)^2",{"lhs":4036,"rhs":4033},"(cos(x)*cos(x) - sin(x)*(-sin(x)))\u002Fcos(x)^2",{"lhs":4038,"rhs":983,"where":4039},"round((tan(x+1e-5) - tan(x-1e-5))\u002F(2e-5) - 1\u002Fcos(x)^2, 6)",{"x":4040},1,{"lhs":4038,"rhs":983,"where":4042},{"x":4043},-0.5,{"lhs":4045,"rhs":603},"1\u002Fcos(pi\u002F4)^2",{"lhs":4047,"rhs":603},"1 + tan(pi\u002F4)^2",{"lhs":4049,"rhs":983,"where":4050},"round((tan(3*(x+1e-5)) - tan(3*(x-1e-5)))\u002F(2e-5) - 3\u002Fcos(3*x)^2, 6)",{"x":4051},0.2,"x \\neq \\frac{\\pi}{2} + k\\pi,\\ k \\in \\mathbb{Z},\\ x \\text{ im Bogenmaß}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>π\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>π\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\neq \\frac{\\pi}{2} + k\\pi,\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:1.0404em;vertical-align:-0.345em;\">\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:0.6954em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\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:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\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:0.345em;\">\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:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\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>k\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">Z\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\in \\mathbb{Z},\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:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">Z\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\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>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">im Bogenmaß\u003C\u002Fspan>",null,"md","derivative-tangent","f(x) = \\tan x \\;\\Rightarrow\\; f'(x) = \\frac{1}{\\cos^2 x} = 1 + \\tan^2 x","\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>\u003Cmi>tan\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\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>\u003Cmn>1\u003C\u002Fmn>\u003Cmrow>\u003Cmsup>\u003Cmrow>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmrow>\u003Cmi>tan\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x) = \\tan x \\;\\Rightarrow\\; f'(x) = \\frac{1}{\\cos^2 x} = 1 + \\tan^2 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: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:0.6151em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">tan\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:2.0074em;vertical-align:-0.686em;\">\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:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7401em;\">\u003Cspan style=\"top:-2.989em;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>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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\">1\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:0.686em;\">\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=\"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:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop\">tan\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\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\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-tangens",[],[4065,4066,4067,4068],"tangent-quotient","quotient-rule","pythagorean-identity","derivative-cosine",{"title":548,"description":4024},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-tangens","Die Ableitung des Tangens ist 1 durch Kosinus zum Quadrat, gleichwertig 1 plus Tangens zum Quadrat.",[4073,4074,4075,4076],"ableitung","tangens","trigonometrische funktion","quotientenregel",[4078,4081,4084],{"symbol":589,"meaning":4079,"symbolHtml":4080},"Winkel im Bogenmaß, an dem der Kosinus nicht null ist","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":609,"meaning":4082,"symbolHtml":4083},"beliebige ganze Zahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4085,"meaning":4086,"symbolHtml":4087},"f'(x)","Ableitung von f","\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>","Nno9y8guLmWHGZq3Rk0nuOwmXkLJLPbHwYVZEt8hASY",[4090,4093,4096,4099],{"stem":4091,"title":4092,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-kosinus","Ableitung des Kosinus",{"stem":4094,"title":4095,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fquotientenregel","Quotientenregel",{"stem":4097,"title":4098,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Ftangens-als-quotient","Tangens als Quotient von Sinus und Kosinus",{"stem":4100,"title":4101,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Ftrigonometrischer-pythagoras","Trigonometrischer Pythagoras",1793824280791]