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a)}{h}",[571,903,905,1079],{"className":904,"ariaHidden":601},[600],[571,906,908,912,1026,1029,1064,1067,1072,1076],{"className":907},[605],[571,909],{"className":910,"style":911},[609],"height:2.0574em;vertical-align:-0.686em;",[571,913,915,920,1022],{"className":914},[614],[571,916],{"className":917},[918,919],"mopen","nulldelimiter",[571,921,923],{"className":922},[796],[571,924,927,1013],{"className":925},[660,926],"vlist-t2",[571,928,930,1008],{"className":929},[664],[571,931,934,982,993],{"className":932,"style":933},[668],"height:1.3714em;",[571,935,937,940],{"style":936},"top:-2.314em;",[571,938],{"className":939,"style":676},[675],[571,941,943,947],{"className":942},[614],[571,944,803],{"className":945,"style":946},[614],"margin-right:0.0556em;",[571,948,950],{"className":949},[614,656],[571,951,953],{"className":952},[660],[571,954,956],{"className":955},[664],[571,957,959,967],{"className":958,"style":652},[668],[571,960,961,964],{"style":671},[571,962],{"className":963,"style":676},[675],[571,965,725],{"className":966,"style":760},[614,615],[571,968,969,972],{"style":671},[571,970],{"className":971,"style":676},[675],[571,973,975],{"className":974,"style":769},[688],[571,976,978],{"className":977,"style":694},[693],[696,979,980],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,981],{"d":707},[571,983,985,988],{"style":984},"top:-3.23em;",[571,986],{"className":987,"style":676},[675],[571,989],{"className":990,"style":992},[991],"frac-line","border-bottom-width:0.04em;",[571,994,996,999],{"style":995},"top:-3.677em;",[571,997],{"className":998,"style":676},[675],[571,1000,1002,1005],{"className":1001},[614],[571,1003,803],{"className":1004,"style":946},[614],[571,1006,592],{"className":1007,"style":616},[614,615],[571,1009,1012],{"className":1010},[1011],"vlist-s","​",[571,1014,1016],{"className":1015},[664],[571,1017,1020],{"className":1018,"style":1019},[668],"height:0.686em;",[571,1021],{},[571,1023],{"className":1024},[1025,919],"mclose",[571,1027,819],{"className":1028},[918],[571,1030,1032],{"className":1031},[614,656],[571,1033,1035],{"className":1034},[660],[571,1036,1038],{"className":1037},[664],[571,1039,1041,1049],{"className":1040,"style":652},[668],[571,1042,1043,1046],{"style":671},[571,1044],{"className":1045,"style":676},[675],[571,1047,635],{"className":1048},[614,615],[571,1050,1051,1054],{"style":671},[571,1052],{"className":1053,"style":676},[675],[571,1055,1057],{"className":1056,"style":689},[688],[571,1058,1060],{"className":1059,"style":694},[693],[696,1061,1062],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1063],{"d":707},[571,1065,828],{"className":1066},[1025],[571,1068],{"className":1069,"style":1071},[1070],"mspace","margin-right:0.2778em;",[571,1073,831],{"className":1074},[1075],"mrel",[571,1077],{"className":1078,"style":1071},[1070],[571,1080,1082,1086,1148,1152],{"className":1081},[605],[571,1083],{"className":1084,"style":1085},[609],"height:2.1791em;vertical-align:-0.7521em;",[571,1087,1091],{"className":1088},[1089,1090],"mop","op-limits",[571,1092,1094,1139],{"className":1093},[660,926],[571,1095,1097,1136],{"className":1096},[664],[571,1098,1101,1126],{"className":1099,"style":1100},[668],"height:0.6944em;",[571,1102,1104,1107],{"style":1103},"top:-2.3479em;margin-left:0em;",[571,1105],{"className":1106,"style":676},[675],[571,1108,1114],{"className":1109},[1110,1111,1112,1113],"sizing","reset-size6","size3","mtight",[571,1115,1117,1120,1123],{"className":1116},[614,1113],[571,1118,847],{"className":1119},[614,615,1113],[571,1121,850],{"className":1122},[1075,1113],[571,1124,854],{"className":1125},[614,1113],[571,1127,1128,1131],{"style":671},[571,1129],{"className":1130,"style":676},[675],[571,1132,1133],{},[571,1134,839],{"className":1135},[1089],[571,1137,1012],{"className":1138},[1011],[571,1140,1142],{"className":1141},[664],[571,1143,1146],{"className":1144,"style":1145},[668],"height:0.7521em;",[571,1147],{},[571,1149],{"className":1150,"style":1151},[1070],"margin-right:0.1667em;",[571,1153,1155,1158,1355],{"className":1154},[614],[571,1156],{"className":1157},[918,919],[571,1159,1161],{"className":1160},[796],[571,1162,1164,1347],{"className":1163},[660,926],[571,1165,1167,1344],{"className":1166},[664],[571,1168,1171,1182,1190],{"className":1169,"style":1170},[668],"height:1.427em;",[571,1172,1173,1176],{"style":936},[571,1174],{"className":1175,"style":676},[675],[571,1177,1179],{"className":1178},[614],[571,1180,847],{"className":1181},[614,615],[571,1183,1184,1187],{"style":984},[571,1185],{"className":1186,"style":676},[675],[571,1188],{"className":1189,"style":992},[991],[571,1191,1192,1195],{"style":995},[571,1193],{"className":1194,"style":676},[675],[571,1196,1198,1201,1204,1239,1243,1247,1250,1253,1288,1291,1294,1297,1300,1303,1306,1341],{"className":1197},[614],[571,1199,592],{"className":1200,"style":616},[614,615],[571,1202,819],{"className":1203},[918],[571,1205,1207],{"className":1206},[614,656],[571,1208,1210],{"className":1209},[660],[571,1211,1213],{"className":1212},[664],[571,1214,1216,1224],{"className":1215,"style":652},[668],[571,1217,1218,1221],{"style":671},[571,1219],{"className":1220,"style":676},[675],[571,1222,635],{"className":1223},[614,615],[571,1225,1226,1229],{"style":671},[571,1227],{"className":1228,"style":676},[675],[571,1230,1232],{"className":1231,"style":689},[688],[571,1233,1235],{"className":1234,"style":694},[693],[696,1236,1237],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1238],{"d":707},[571,1240],{"className":1241,"style":1242},[1070],"margin-right:0.2222em;",[571,1244,871],{"className":1245},[1246],"mbin",[571,1248],{"className":1249,"style":1242},[1070],[571,1251,847],{"className":1252},[614,615],[571,1254,1256],{"className":1255},[614,656],[571,1257,1259],{"className":1258},[660],[571,1260,1262],{"className":1261},[664],[571,1263,1265,1273],{"className":1264,"style":652},[668],[571,1266,1267,1270],{"style":671},[571,1268],{"className":1269,"style":676},[675],[571,1271,725],{"className":1272,"style":760},[614,615],[571,1274,1275,1278],{"style":671},[571,1276],{"className":1277,"style":676},[675],[571,1279,1281],{"className":1280,"style":769},[688],[571,1282,1284],{"className":1283,"style":694},[693],[696,1285,1286],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1287],{"d":707},[571,1289,828],{"className":1290},[1025],[571,1292],{"className":1293,"style":1242},[1070],[571,1295,884],{"className":1296},[1246],[571,1298],{"className":1299,"style":1242},[1070],[571,1301,592],{"className":1302,"style":616},[614,615],[571,1304,819],{"className":1305},[918],[571,1307,1309],{"className":1308},[614,656],[571,1310,1312],{"className":1311},[660],[571,1313,1315],{"className":1314},[664],[571,1316,1318,1326],{"className":1317,"style":652},[668],[571,1319,1320,1323],{"style":671},[571,1321],{"className":1322,"style":676},[675],[571,1324,635],{"className":1325},[614,615],[571,1327,1328,1331],{"style":671},[571,1329],{"className":1330,"style":676},[675],[571,1332,1334],{"className":1333,"style":689},[688],[571,1335,1337],{"className":1336,"style":694},[693],[696,1338,1339],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1340],{"d":707},[571,1342,828],{"className":1343},[1025],[571,1345,1012],{"className":1346},[1011],[571,1348,1350],{"className":1349},[664],[571,1351,1353],{"className":1352,"style":1019},[668],[571,1354],{},[571,1356],{"className":1357},[1025,919],[563,1359,1360,1361,1389],{},"Ist ",[571,1362,1364,1377],{"className":1363},[574],[571,1365,1367],{"className":1366},[578],[580,1368,1369],{"xmlns":582},[584,1370,1371,1375],{},[587,1372,1373],{},[590,1374,592],{},[594,1376,592],{"encoding":596},[571,1378,1380],{"className":1379,"ariaHidden":601},[600],[571,1381,1383,1386],{"className":1382},[605],[571,1384],{"className":1385,"style":610},[609],[571,1387,592],{"className":1388,"style":616},[614,615]," differenzierbar, lässt sie sich einfach als Skalarprodukt mit dem Gradienten berechnen. Die partiellen Ableitungen sind Sonderfälle mit den Einheitsvektoren der Koordinatenachsen als Richtung.",[563,1391,1392,1393,1545,1546,1587],{},"Aus ",[571,1394,1396,1441],{"className":1395},[574],[571,1397,1399],{"className":1398},[578],[580,1400,1401],{"xmlns":582},[584,1402,1403,1438],{},[587,1404,1405,1408,1410,1413,1419,1421,1424,1426,1428,1430,1433,1435],{},[590,1406,1407],{"mathvariant":802},"∇",[590,1409,592],{},[637,1411,1412],{},"⋅",[631,1414,1415,1417],{"accent":601},[590,1416,725],{},[637,1418,639],{},[637,1420,831],{},[590,1422,1423],{"mathvariant":802},"∣",[590,1425,1407],{"mathvariant":802},[590,1427,592],{},[590,1429,1423],{"mathvariant":802},[590,1431,1432],{},"cos",[637,1434,842],{},[590,1436,1437],{},"α",[594,1439,1440],{"encoding":596},"\\nabla f \\cdot \\vec v = |\\nabla f| \\cos \\alpha",[571,1442,1444,1465,1515],{"className":1443,"ariaHidden":601},[600],[571,1445,1447,1450,1453,1456,1459,1462],{"className":1446},[605],[571,1448],{"className":1449,"style":610},[609],[571,1451,1407],{"className":1452},[614],[571,1454,592],{"className":1455,"style":616},[614,615],[571,1457],{"className":1458,"style":1242},[1070],[571,1460,1412],{"className":1461},[1246],[571,1463],{"className":1464,"style":1242},[1070],[571,1466,1468,1471,1506,1509,1512],{"className":1467},[605],[571,1469],{"className":1470,"style":652},[609],[571,1472,1474],{"className":1473},[614,656],[571,1475,1477],{"className":1476},[660],[571,1478,1480],{"className":1479},[664],[571,1481,1483,1491],{"className":1482,"style":652},[668],[571,1484,1485,1488],{"style":671},[571,1486],{"className":1487,"style":676},[675],[571,1489,725],{"className":1490,"style":760},[614,615],[571,1492,1493,1496],{"style":671},[571,1494],{"className":1495,"style":676},[675],[571,1497,1499],{"className":1498,"style":769},[688],[571,1500,1502],{"className":1501,"style":694},[693],[696,1503,1504],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1505],{"d":707},[571,1507],{"className":1508,"style":1071},[1070],[571,1510,831],{"className":1511},[1075],[571,1513],{"className":1514,"style":1071},[1070],[571,1516,1518,1522,1526,1529,1532,1535,1538,1541],{"className":1517},[605],[571,1519],{"className":1520,"style":1521},[609],"height:1em;vertical-align:-0.25em;",[571,1523,1525],{"className":1524},[614],"∣∇",[571,1527,592],{"className":1528,"style":616},[614,615],[571,1530,1423],{"className":1531},[614],[571,1533],{"className":1534,"style":1151},[1070],[571,1536,1432],{"className":1537},[1089],[571,1539],{"className":1540,"style":1151},[1070],[571,1542,1437],{"className":1543,"style":1544},[614,615],"margin-right:0.0037em;"," folgt: Die Richtungsableitung ist am größten in Richtung des Gradienten (Wert ",[571,1547,1549,1569],{"className":1548},[574],[571,1550,1552],{"className":1551},[578],[580,1553,1554],{"xmlns":582},[584,1555,1556,1566],{},[587,1557,1558,1560,1562,1564],{},[590,1559,1423],{"mathvariant":802},[590,1561,1407],{"mathvariant":802},[590,1563,592],{},[590,1565,1423],{"mathvariant":802},[594,1567,1568],{"encoding":596},"|\\nabla f|",[571,1570,1572],{"className":1571,"ariaHidden":601},[600],[571,1573,1575,1578,1581,1584],{"className":1574},[605],[571,1576],{"className":1577,"style":1521},[609],[571,1579,1525],{"className":1580},[614],[571,1582,592],{"className":1583,"style":616},[614,615],[571,1585,1423],{"className":1586},[614],"), am kleinsten in der Gegenrichtung und null senkrecht dazu, also entlang der Höhenlinie.",[563,1589,1590,1591,1594,1595,1765,1766,2013],{},"Die Richtung muss ein ",[567,1592,1593],{},"Einheitsvektor"," sein. Ein beliebiger Vektor ",[571,1596,1598,1626],{"className":1597},[574],[571,1599,1601],{"className":1600},[578],[580,1602,1603],{"xmlns":582},[584,1604,1605,1623],{},[587,1606,1607,1614,1617],{},[631,1608,1609,1612],{"accent":601},[590,1610,1611],{},"w",[637,1613,639],{},[637,1615,1616],{"mathvariant":802},"≠",[631,1618,1619,1621],{"accent":601},[852,1620,854],{},[637,1622,639],{},[594,1624,1625],{"encoding":596},"\\vec w \\neq \\vec 0",[571,1627,1629,1722],{"className":1628,"ariaHidden":601},[600],[571,1630,1632,1636,1673,1676,1719],{"className":1631},[605],[571,1633],{"className":1634,"style":1635},[609],"height:0.9084em;vertical-align:-0.1944em;",[571,1637,1639],{"className":1638},[614,656],[571,1640,1642],{"className":1641},[660],[571,1643,1645],{"className":1644},[664],[571,1646,1648,1657],{"className":1647,"style":652},[668],[571,1649,1650,1653],{"style":671},[571,1651],{"className":1652,"style":676},[675],[571,1654,1611],{"className":1655,"style":1656},[614,615],"margin-right:0.0269em;",[571,1658,1659,1662],{"style":671},[571,1660],{"className":1661,"style":676},[675],[571,1663,1666],{"className":1664,"style":1665},[688],"left:-0.1522em;",[571,1667,1669],{"className":1668,"style":694},[693],[696,1670,1671],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1672],{"d":707},[571,1674],{"className":1675,"style":1071},[1070],[571,1677,1679,1712,1716],{"className":1678},[1075],[571,1680,1682],{"className":1681},[1075],[571,1683,1686],{"className":1684},[614,1685],"vbox",[571,1687,1690],{"className":1688},[1689],"thinbox",[571,1691,1694,1697,1708],{"className":1692},[1693],"rlap",[571,1695],{"className":1696,"style":610},[609],[571,1698,1701],{"className":1699},[1700],"inner",[571,1702,1704],{"className":1703},[614],[571,1705,1707],{"className":1706},[1075],"",[571,1709],{"className":1710},[1711],"fix",[571,1713],{"className":1714},[1070,1715],"nobreak",[571,1717,831],{"className":1718},[1075],[571,1720],{"className":1721,"style":1071},[1070],[571,1723,1725,1729],{"className":1724},[605],[571,1726],{"className":1727,"style":1728},[609],"height:0.9274em;",[571,1730,1732],{"className":1731},[614,656],[571,1733,1735],{"className":1734},[660],[571,1736,1738],{"className":1737},[664],[571,1739,1741,1749],{"className":1740,"style":1728},[668],[571,1742,1743,1746],{"style":671},[571,1744],{"className":1745,"style":676},[675],[571,1747,854],{"className":1748},[614],[571,1750,1752,1755],{"style":1751},"top:-3.2134em;",[571,1753],{"className":1754,"style":676},[675],[571,1756,1758],{"className":1757,"style":689},[688],[571,1759,1761],{"className":1760,"style":694},[693],[696,1762,1763],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1764],{"d":707}," wird vorher normiert: ",[571,1767,1769,1809],{"className":1768},[574],[571,1770,1772],{"className":1771},[578],[580,1773,1774],{"xmlns":582},[584,1775,1776,1806],{},[587,1777,1778,1784,1786],{},[631,1779,1780,1782],{"accent":601},[590,1781,725],{},[637,1783,639],{},[637,1785,831],{},[796,1787,1788,1794],{},[631,1789,1790,1792],{"accent":601},[590,1791,1611],{},[637,1793,639],{},[587,1795,1796,1798,1804],{},[590,1797,1423],{"mathvariant":802},[631,1799,1800,1802],{"accent":601},[590,1801,1611],{},[637,1803,639],{},[590,1805,1423],{"mathvariant":802},[594,1807,1808],{"encoding":596},"\\vec v = \\frac{\\vec w}{|\\vec w|}",[571,1810,1812,1862],{"className":1811,"ariaHidden":601},[600],[571,1813,1815,1818,1853,1856,1859],{"className":1814},[605],[571,1816],{"className":1817,"style":652},[609],[571,1819,1821],{"className":1820},[614,656],[571,1822,1824],{"className":1823},[660],[571,1825,1827],{"className":1826},[664],[571,1828,1830,1838],{"className":1829,"style":652},[668],[571,1831,1832,1835],{"style":671},[571,1833],{"className":1834,"style":676},[675],[571,1836,725],{"className":1837,"style":760},[614,615],[571,1839,1840,1843],{"style":671},[571,1841],{"className":1842,"style":676},[675],[571,1844,1846],{"className":1845,"style":769},[688],[571,1847,1849],{"className":1848,"style":694},[693],[696,1850,1851],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1852],{"d":707},[571,1854],{"className":1855,"style":1071},[1070],[571,1857,831],{"className":1858},[1075],[571,1860],{"className":1861,"style":1071},[1070],[571,1863,1865,1869],{"className":1864},[605],[571,1866],{"className":1867,"style":1868},[609],"height:1.4138em;vertical-align:-0.52em;",[571,1870,1872,1875,2010],{"className":1871},[614],[571,1873],{"className":1874},[918,919],[571,1876,1878],{"className":1877},[796],[571,1879,1881,2001],{"className":1880},[660,926],[571,1882,1884,1998],{"className":1883},[664],[571,1885,1888,1943,1951],{"className":1886,"style":1887},[668],"height:0.8938em;",[571,1889,1891,1894],{"style":1890},"top:-2.655em;",[571,1892],{"className":1893,"style":676},[675],[571,1895,1897],{"className":1896},[1110,1111,1112,1113],[571,1898,1900,1903,1940],{"className":1899},[614,1113],[571,1901,1423],{"className":1902},[614,1113],[571,1904,1906],{"className":1905},[614,656,1113],[571,1907,1909],{"className":1908},[660],[571,1910,1912],{"className":1911},[664],[571,1913,1915,1925],{"className":1914,"style":652},[668],[571,1916,1918,1922],{"style":1917},"top:-2.714em;",[571,1919],{"className":1920,"style":1921},[675],"height:2.714em;",[571,1923,1611],{"className":1924,"style":1656},[614,615,1113],[571,1926,1927,1930],{"style":1917},[571,1928],{"className":1929,"style":1921},[675],[571,1931,1933],{"className":1932,"style":1665},[688],[571,1934,1936],{"className":1935,"style":694},[693,1113],[696,1937,1938],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1939],{"d":707},[571,1941,1423],{"className":1942},[614,1113],[571,1944,1945,1948],{"style":984},[571,1946],{"className":1947,"style":676},[675],[571,1949],{"className":1950,"style":992},[991],[571,1952,1954,1957],{"style":1953},"top:-3.394em;",[571,1955],{"className":1956,"style":676},[675],[571,1958,1960],{"className":1959},[1110,1111,1112,1113],[571,1961,1963],{"className":1962},[614,1113],[571,1964,1966],{"className":1965},[614,656,1113],[571,1967,1969],{"className":1968},[660],[571,1970,1972],{"className":1971},[664],[571,1973,1975,1983],{"className":1974,"style":652},[668],[571,1976,1977,1980],{"style":1917},[571,1978],{"className":1979,"style":1921},[675],[571,1981,1611],{"className":1982,"style":1656},[614,615,1113],[571,1984,1985,1988],{"style":1917},[571,1986],{"className":1987,"style":1921},[675],[571,1989,1991],{"className":1990,"style":1665},[688],[571,1992,1994],{"className":1993,"style":694},[693,1113],[696,1995,1996],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1997],{"d":707},[571,1999,1012],{"className":2000},[1011],[571,2002,2004],{"className":2003},[664],[571,2005,2008],{"className":2006,"style":2007},[668],"height:0.52em;",[571,2009],{},[571,2011],{"className":2012},[1025,919],".",[558,2015,2017],{"id":2016},"beispiele","Beispiele",[563,2019,2020,2021,2200,2201,2345,2346,2486,2487,2200,2586,2755],{},"Für ",[571,2022,2024,2072],{"className":2023},[574],[571,2025,2027],{"className":2026},[578],[580,2028,2029],{"xmlns":582},[584,2030,2031,2069],{},[587,2032,2033,2035,2037,2040,2043,2046,2048,2050,2058,2060,2063],{},[590,2034,592],{},[637,2036,819],{"stretchy":818},[590,2038,2039],{},"x",[637,2041,2042],{"separator":601},",",[590,2044,2045],{},"y",[637,2047,828],{"stretchy":818},[637,2049,831],{},[2051,2052,2053,2055],"msup",{},[590,2054,2039],{},[852,2056,2057],{},"2",[637,2059,871],{},[852,2061,2062],{},"3",[2051,2064,2065,2067],{},[590,2066,2045],{},[852,2068,2057],{},[594,2070,2071],{"encoding":596},"f(x, y) = x^2 + 3y^2",[571,2073,2075,2112,2161],{"className":2074,"ariaHidden":601},[600],[571,2076,2078,2081,2084,2087,2090,2094,2097,2100,2103,2106,2109],{"className":2077},[605],[571,2079],{"className":2080,"style":1521},[609],[571,2082,592],{"className":2083,"style":616},[614,615],[571,2085,819],{"className":2086},[918],[571,2088,2039],{"className":2089},[614,615],[571,2091,2042],{"className":2092},[2093],"mpunct",[571,2095],{"className":2096,"style":1151},[1070],[571,2098,2045],{"className":2099,"style":760},[614,615],[571,2101,828],{"className":2102},[1025],[571,2104],{"className":2105,"style":1071},[1070],[571,2107,831],{"className":2108},[1075],[571,2110],{"className":2111,"style":1071},[1070],[571,2113,2115,2119,2152,2155,2158],{"className":2114},[605],[571,2116],{"className":2117,"style":2118},[609],"height:0.8974em;vertical-align:-0.0833em;",[571,2120,2122,2125],{"className":2121},[614],[571,2123,2039],{"className":2124},[614,615],[571,2126,2129],{"className":2127},[2128],"msupsub",[571,2130,2132],{"className":2131},[660],[571,2133,2135],{"className":2134},[664],[571,2136,2139],{"className":2137,"style":2138},[668],"height:0.8141em;",[571,2140,2142,2146],{"style":2141},"top:-3.063em;margin-right:0.05em;",[571,2143],{"className":2144,"style":2145},[675],"height:2.7em;",[571,2147,2149],{"className":2148},[1110,1111,1112,1113],[571,2150,2057],{"className":2151},[614,1113],[571,2153],{"className":2154,"style":1242},[1070],[571,2156,871],{"className":2157},[1246],[571,2159],{"className":2160,"style":1242},[1070],[571,2162,2164,2168,2171],{"className":2163},[605],[571,2165],{"className":2166,"style":2167},[609],"height:1.0085em;vertical-align:-0.1944em;",[571,2169,2062],{"className":2170},[614],[571,2172,2174,2177],{"className":2173},[614],[571,2175,2045],{"className":2176,"style":760},[614,615],[571,2178,2180],{"className":2179},[2128],[571,2181,2183],{"className":2182},[660],[571,2184,2186],{"className":2185},[664],[571,2187,2189],{"className":2188,"style":2138},[668],[571,2190,2191,2194],{"style":2141},[571,2192],{"className":2193,"style":2145},[675],[571,2195,2197],{"className":2196},[1110,1111,1112,1113],[571,2198,2057],{"className":2199},[614,1113]," ist ",[571,2202,2204,2250],{"className":2203},[574],[571,2205,2207],{"className":2206},[578],[580,2208,2209],{"xmlns":582},[584,2210,2211,2247],{},[587,2212,2213,2215,2217,2219,2221,2223,2226,2228,2230,2232,2235,2237,2240],{},[590,2214,1407],{"mathvariant":802},[590,2216,592],{},[637,2218,819],{"stretchy":818},[852,2220,2057],{},[637,2222,2042],{"separator":601},[852,2224,2225],{},"1",[637,2227,828],{"stretchy":818},[637,2229,831],{},[637,2231,819],{"stretchy":818},[852,2233,2234],{},"4",[637,2236,2042],{"separator":601},[852,2238,2239],{},"6",[2051,2241,2242,2244],{},[637,2243,828],{"stretchy":818},[590,2245,2246],{},"T",[594,2248,2249],{"encoding":596},"\\nabla f(2, 1) = (4, 6)^T",[571,2251,2253,2292],{"className":2252,"ariaHidden":601},[600],[571,2254,2256,2259,2262,2265,2268,2271,2274,2277,2280,2283,2286,2289],{"className":2255},[605],[571,2257],{"className":2258,"style":1521},[609],[571,2260,1407],{"className":2261},[614],[571,2263,592],{"className":2264,"style":616},[614,615],[571,2266,819],{"className":2267},[918],[571,2269,2057],{"className":2270},[614],[571,2272,2042],{"className":2273},[2093],[571,2275],{"className":2276,"style":1151},[1070],[571,2278,2225],{"className":2279},[614],[571,2281,828],{"className":2282},[1025],[571,2284],{"className":2285,"style":1071},[1070],[571,2287,831],{"className":2288},[1075],[571,2290],{"className":2291,"style":1071},[1070],[571,2293,2295,2299,2302,2305,2308,2311,2314],{"className":2294},[605],[571,2296],{"className":2297,"style":2298},[609],"height:1.0913em;vertical-align:-0.25em;",[571,2300,819],{"className":2301},[918],[571,2303,2234],{"className":2304},[614],[571,2306,2042],{"className":2307},[2093],[571,2309],{"className":2310,"style":1151},[1070],[571,2312,2239],{"className":2313},[614],[571,2315,2317,2320],{"className":2316},[1025],[571,2318,828],{"className":2319},[1025],[571,2321,2323],{"className":2322},[2128],[571,2324,2326],{"className":2325},[660],[571,2327,2329],{"className":2328},[664],[571,2330,2333],{"className":2331,"style":2332},[668],"height:0.8413em;",[571,2334,2335,2338],{"style":2141},[571,2336],{"className":2337,"style":2145},[675],[571,2339,2341],{"className":2340},[1110,1111,1112,1113],[571,2342,2246],{"className":2343,"style":2344},[614,615,1113],"margin-right:0.1389em;",". Gesucht ist die Steigung in Richtung ",[571,2347,2349,2383],{"className":2348},[574],[571,2350,2352],{"className":2351},[578],[580,2353,2354],{"xmlns":582},[584,2355,2356,2380],{},[587,2357,2358,2364,2366,2368,2370,2372,2374],{},[631,2359,2360,2362],{"accent":601},[590,2361,1611],{},[637,2363,639],{},[637,2365,831],{},[637,2367,819],{"stretchy":818},[852,2369,2062],{},[637,2371,2042],{"separator":601},[852,2373,2234],{},[2051,2375,2376,2378],{},[637,2377,828],{"stretchy":818},[590,2379,2246],{},[594,2381,2382],{"encoding":596},"\\vec w = (3, 4)^T",[571,2384,2386,2436],{"className":2385,"ariaHidden":601},[600],[571,2387,2389,2392,2427,2430,2433],{"className":2388},[605],[571,2390],{"className":2391,"style":652},[609],[571,2393,2395],{"className":2394},[614,656],[571,2396,2398],{"className":2397},[660],[571,2399,2401],{"className":2400},[664],[571,2402,2404,2412],{"className":2403,"style":652},[668],[571,2405,2406,2409],{"style":671},[571,2407],{"className":2408,"style":676},[675],[571,2410,1611],{"className":2411,"style":1656},[614,615],[571,2413,2414,2417],{"style":671},[571,2415],{"className":2416,"style":676},[675],[571,2418,2420],{"className":2419,"style":1665},[688],[571,2421,2423],{"className":2422,"style":694},[693],[696,2424,2425],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2426],{"d":707},[571,2428],{"className":2429,"style":1071},[1070],[571,2431,831],{"className":2432},[1075],[571,2434],{"className":2435,"style":1071},[1070],[571,2437,2439,2442,2445,2448,2451,2454,2457],{"className":2438},[605],[571,2440],{"className":2441,"style":2298},[609],[571,2443,819],{"className":2444},[918],[571,2446,2062],{"className":2447},[614],[571,2449,2042],{"className":2450},[2093],[571,2452],{"className":2453,"style":1151},[1070],[571,2455,2234],{"className":2456},[614],[571,2458,2460,2463],{"className":2459},[1025],[571,2461,828],{"className":2462},[1025],[571,2464,2466],{"className":2465},[2128],[571,2467,2469],{"className":2468},[660],[571,2470,2472],{"className":2471},[664],[571,2473,2475],{"className":2474,"style":2332},[668],[571,2476,2477,2480],{"style":2141},[571,2478],{"className":2479,"style":2145},[675],[571,2481,2483],{"className":2482},[1110,1111,1112,1113],[571,2484,2246],{"className":2485,"style":2344},[614,615,1113],". Wegen ",[571,2488,2490,2517],{"className":2489},[574],[571,2491,2493],{"className":2492},[578],[580,2494,2495],{"xmlns":582},[584,2496,2497,2514],{},[587,2498,2499,2501,2507,2509,2511],{},[590,2500,1423],{"mathvariant":802},[631,2502,2503,2505],{"accent":601},[590,2504,1611],{},[637,2506,639],{},[590,2508,1423],{"mathvariant":802},[637,2510,831],{},[852,2512,2513],{},"5",[594,2515,2516],{"encoding":596},"|\\vec w| = 5",[571,2518,2520,2576],{"className":2519,"ariaHidden":601},[600],[571,2521,2523,2526,2529,2564,2567,2570,2573],{"className":2522},[605],[571,2524],{"className":2525,"style":1521},[609],[571,2527,1423],{"className":2528},[614],[571,2530,2532],{"className":2531},[614,656],[571,2533,2535],{"className":2534},[660],[571,2536,2538],{"className":2537},[664],[571,2539,2541,2549],{"className":2540,"style":652},[668],[571,2542,2543,2546],{"style":671},[571,2544],{"className":2545,"style":676},[675],[571,2547,1611],{"className":2548,"style":1656},[614,615],[571,2550,2551,2554],{"style":671},[571,2552],{"className":2553,"style":676},[675],[571,2555,2557],{"className":2556,"style":1665},[688],[571,2558,2560],{"className":2559,"style":694},[693],[696,2561,2562],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2563],{"d":707},[571,2565,1423],{"className":2566},[614],[571,2568],{"className":2569,"style":1071},[1070],[571,2571,831],{"className":2572},[1075],[571,2574],{"className":2575,"style":1071},[1070],[571,2577,2579,2583],{"className":2578},[605],[571,2580],{"className":2581,"style":2582},[609],"height:0.6444em;",[571,2584,2513],{"className":2585},[614],[571,2587,2589,2630],{"className":2588},[574],[571,2590,2592],{"className":2591},[578],[580,2593,2594],{"xmlns":582},[584,2595,2596,2627],{},[587,2597,2598,2604,2606,2608,2611,2614,2618,2621],{},[631,2599,2600,2602],{"accent":601},[590,2601,725],{},[637,2603,639],{},[637,2605,831],{},[637,2607,819],{"stretchy":818},[852,2609,2610],{},"0,6",[637,2612,2613],{"separator":601},";",[2615,2616,2617],"mtext",{}," ",[852,2619,2620],{},"0,8",[2051,2622,2623,2625],{},[637,2624,828],{"stretchy":818},[590,2626,2246],{},[594,2628,2629],{"encoding":596},"\\vec v = (0{,}6;\\ 0{,}8)^T",[571,2631,2633,2683],{"className":2632,"ariaHidden":601},[600],[571,2634,2636,2639,2674,2677,2680],{"className":2635},[605],[571,2637],{"className":2638,"style":652},[609],[571,2640,2642],{"className":2641},[614,656],[571,2643,2645],{"className":2644},[660],[571,2646,2648],{"className":2647},[664],[571,2649,2651,2659],{"className":2650,"style":652},[668],[571,2652,2653,2656],{"style":671},[571,2654],{"className":2655,"style":676},[675],[571,2657,725],{"className":2658,"style":760},[614,615],[571,2660,2661,2664],{"style":671},[571,2662],{"className":2663,"style":676},[675],[571,2665,2667],{"className":2666,"style":769},[688],[571,2668,2670],{"className":2669,"style":694},[693],[696,2671,2672],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2673],{"d":707},[571,2675],{"className":2676,"style":1071},[1070],[571,2678,831],{"className":2679},[1075],[571,2681],{"className":2682,"style":1071},[1070],[571,2684,2686,2689,2692,2695,2701,2704,2707,2710,2713,2716,2722,2726],{"className":2685},[605],[571,2687],{"className":2688,"style":2298},[609],[571,2690,819],{"className":2691},[918],[571,2693,854],{"className":2694},[614],[571,2696,2698],{"className":2697},[614],[571,2699,2042],{"className":2700},[2093],[571,2702,2239],{"className":2703},[614],[571,2705,2613],{"className":2706},[2093],[571,2708,2617],{"className":2709},[1070],[571,2711],{"className":2712,"style":1151},[1070],[571,2714,854],{"className":2715},[614],[571,2717,2719],{"className":2718},[614],[571,2720,2042],{"className":2721},[2093],[571,2723,2725],{"className":2724},[614],"8",[571,2727,2729,2732],{"className":2728},[1025],[571,2730,828],{"className":2731},[1025],[571,2733,2735],{"className":2734},[2128],[571,2736,2738],{"className":2737},[660],[571,2739,2741],{"className":2740},[664],[571,2742,2744],{"className":2743,"style":2332},[668],[571,2745,2746,2749],{"style":2141},[571,2747],{"className":2748,"style":2145},[675],[571,2750,2752],{"className":2751},[1110,1111,1112,1113],[571,2753,2246],{"className":2754,"style":2344},[614,615,1113],":",[571,2757,2759],{"className":2758},[781],[571,2760,2762,2833],{"className":2761},[574],[571,2763,2765],{"className":2764},[578],[580,2766,2767],{"xmlns":582,"display":790},[584,2768,2769,2830],{},[587,2770,2771,2789,2791,2793,2795,2797,2799,2801,2803,2805,2807,2809,2811,2813,2815,2817,2820,2822,2825,2827],{},[796,2772,2773,2779],{},[587,2774,2775,2777],{},[590,2776,803],{"mathvariant":802},[590,2778,592],{},[587,2780,2781,2783],{},[590,2782,803],{"mathvariant":802},[631,2784,2785,2787],{"accent":601},[590,2786,725],{},[637,2788,639],{},[637,2790,819],{"stretchy":818},[852,2792,2057],{},[637,2794,2042],{"separator":601},[852,2796,2225],{},[637,2798,828],{"stretchy":818},[637,2800,831],{},[852,2802,2234],{},[637,2804,1412],{},[852,2806,2610],{},[637,2808,871],{},[852,2810,2239],{},[637,2812,1412],{},[852,2814,2620],{},[637,2816,831],{},[852,2818,2819],{},"2,4",[637,2821,871],{},[852,2823,2824],{},"4,8",[637,2826,831],{},[852,2828,2829],{},"7,2",[594,2831,2832],{"encoding":596},"\\frac{\\partial f}{\\partial \\vec{v}}(2, 1) = 4 \\cdot 0{,}6 + 6 \\cdot 0{,}8 = 2{,}4 + 4{,}8 = 7{,}2",[571,2834,2836,2969,2987,3015,3033,3060,3087,3114],{"className":2835,"ariaHidden":601},[600],[571,2837,2839,2842,2942,2945,2948,2951,2954,2957,2960,2963,2966],{"className":2838},[605],[571,2840],{"className":2841,"style":911},[609],[571,2843,2845,2848,2939],{"className":2844},[614],[571,2846],{"className":2847},[918,919],[571,2849,2851],{"className":2850},[796],[571,2852,2854,2931],{"className":2853},[660,926],[571,2855,2857,2928],{"className":2856},[664],[571,2858,2860,2906,2914],{"className":2859,"style":933},[668],[571,2861,2862,2865],{"style":936},[571,2863],{"className":2864,"style":676},[675],[571,2866,2868,2871],{"className":2867},[614],[571,2869,803],{"className":2870,"style":946},[614],[571,2872,2874],{"className":2873},[614,656],[571,2875,2877],{"className":2876},[660],[571,2878,2880],{"className":2879},[664],[571,2881,2883,2891],{"className":2882,"style":652},[668],[571,2884,2885,2888],{"style":671},[571,2886],{"className":2887,"style":676},[675],[571,2889,725],{"className":2890,"style":760},[614,615],[571,2892,2893,2896],{"style":671},[571,2894],{"className":2895,"style":676},[675],[571,2897,2899],{"className":2898,"style":769},[688],[571,2900,2902],{"className":2901,"style":694},[693],[696,2903,2904],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2905],{"d":707},[571,2907,2908,2911],{"style":984},[571,2909],{"className":2910,"style":676},[675],[571,2912],{"className":2913,"style":992},[991],[571,2915,2916,2919],{"style":995},[571,2917],{"className":2918,"style":676},[675],[571,2920,2922,2925],{"className":2921},[614],[571,2923,803],{"className":2924,"style":946},[614],[571,2926,592],{"className":2927,"style":616},[614,615],[571,2929,1012],{"className":2930},[1011],[571,2932,2934],{"className":2933},[664],[571,2935,2937],{"className":2936,"style":1019},[668],[571,2938],{},[571,2940],{"className":2941},[1025,919],[571,2943,819],{"className":2944},[918],[571,2946,2057],{"className":2947},[614],[571,2949,2042],{"className":2950},[2093],[571,2952],{"className":2953,"style":1151},[1070],[571,2955,2225],{"className":2956},[614],[571,2958,828],{"className":2959},[1025],[571,2961],{"className":2962,"style":1071},[1070],[571,2964,831],{"className":2965},[1075],[571,2967],{"className":2968,"style":1071},[1070],[571,2970,2972,2975,2978,2981,2984],{"className":2971},[605],[571,2973],{"className":2974,"style":2582},[609],[571,2976,2234],{"className":2977},[614],[571,2979],{"className":2980,"style":1242},[1070],[571,2982,1412],{"className":2983},[1246],[571,2985],{"className":2986,"style":1242},[1070],[571,2988,2990,2994,2997,3003,3006,3009,3012],{"className":2989},[605],[571,2991],{"className":2992,"style":2993},[609],"height:0.8389em;vertical-align:-0.1944em;",[571,2995,854],{"className":2996},[614],[571,2998,3000],{"className":2999},[614],[571,3001,2042],{"className":3002},[2093],[571,3004,2239],{"className":3005},[614],[571,3007],{"className":3008,"style":1242},[1070],[571,3010,871],{"className":3011},[1246],[571,3013],{"className":3014,"style":1242},[1070],[571,3016,3018,3021,3024,3027,3030],{"className":3017},[605],[571,3019],{"className":3020,"style":2582},[609],[571,3022,2239],{"className":3023},[614],[571,3025],{"className":3026,"style":1242},[1070],[571,3028,1412],{"className":3029},[1246],[571,3031],{"className":3032,"style":1242},[1070],[571,3034,3036,3039,3042,3048,3051,3054,3057],{"className":3035},[605],[571,3037],{"className":3038,"style":2993},[609],[571,3040,854],{"className":3041},[614],[571,3043,3045],{"className":3044},[614],[571,3046,2042],{"className":3047},[2093],[571,3049,2725],{"className":3050},[614],[571,3052],{"className":3053,"style":1071},[1070],[571,3055,831],{"className":3056},[1075],[571,3058],{"className":3059,"style":1071},[1070],[571,3061,3063,3066,3069,3075,3078,3081,3084],{"className":3062},[605],[571,3064],{"className":3065,"style":2993},[609],[571,3067,2057],{"className":3068},[614],[571,3070,3072],{"className":3071},[614],[571,3073,2042],{"className":3074},[2093],[571,3076,2234],{"className":3077},[614],[571,3079],{"className":3080,"style":1242},[1070],[571,3082,871],{"className":3083},[1246],[571,3085],{"className":3086,"style":1242},[1070],[571,3088,3090,3093,3096,3102,3105,3108,3111],{"className":3089},[605],[571,3091],{"className":3092,"style":2993},[609],[571,3094,2234],{"className":3095},[614],[571,3097,3099],{"className":3098},[614],[571,3100,2042],{"className":3101},[2093],[571,3103,2725],{"className":3104},[614],[571,3106],{"className":3107,"style":1071},[1070],[571,3109,831],{"className":3110},[1075],[571,3112],{"className":3113,"style":1071},[1070],[571,3115,3117,3120,3124,3130],{"className":3116},[605],[571,3118],{"className":3119,"style":2993},[609],[571,3121,3123],{"className":3122},[614],"7",[571,3125,3127],{"className":3126},[614],[571,3128,2042],{"className":3129},[2093],[571,3131,2057],{"className":3132},[614],[563,3134,3135,3136,3323,3324,3376],{},"Die größte mögliche Steigung in diesem Punkt ist ",[571,3137,3139,3183],{"className":3138},[574],[571,3140,3142],{"className":3141},[578],[580,3143,3144],{"xmlns":582},[584,3145,3146,3180],{},[587,3147,3148,3150,3152,3154,3156,3158,3160,3162,3164,3166,3168,3174,3177],{},[590,3149,1423],{"mathvariant":802},[590,3151,1407],{"mathvariant":802},[590,3153,592],{},[637,3155,819],{"stretchy":818},[852,3157,2057],{},[637,3159,2042],{"separator":601},[852,3161,2225],{},[637,3163,828],{"stretchy":818},[590,3165,1423],{"mathvariant":802},[637,3167,831],{},[3169,3170,3171],"msqrt",{},[852,3172,3173],{},"52",[637,3175,3176],{},"≈",[852,3178,3179],{},"7,21",[594,3181,3182],{"encoding":596},"|\\nabla f(2, 1)| = \\sqrt{52} \\approx 7{,}21",[571,3184,3186,3228,3304],{"className":3185,"ariaHidden":601},[600],[571,3187,3189,3192,3195,3198,3201,3204,3207,3210,3213,3216,3219,3222,3225],{"className":3188},[605],[571,3190],{"className":3191,"style":1521},[609],[571,3193,1525],{"className":3194},[614],[571,3196,592],{"className":3197,"style":616},[614,615],[571,3199,819],{"className":3200},[918],[571,3202,2057],{"className":3203},[614],[571,3205,2042],{"className":3206},[2093],[571,3208],{"className":3209,"style":1151},[1070],[571,3211,2225],{"className":3212},[614],[571,3214,828],{"className":3215},[1025],[571,3217,1423],{"className":3218},[614],[571,3220],{"className":3221,"style":1071},[1070],[571,3223,831],{"className":3224},[1075],[571,3226],{"className":3227,"style":1071},[1070],[571,3229,3231,3235,3295,3298,3301],{"className":3230},[605],[571,3232],{"className":3233,"style":3234},[609],"height:1.04em;vertical-align:-0.1328em;",[571,3236,3239],{"className":3237},[614,3238],"sqrt",[571,3240,3242,3286],{"className":3241},[660,926],[571,3243,3245,3283],{"className":3244},[664],[571,3246,3249,3263],{"className":3247,"style":3248},[668],"height:0.9072em;",[571,3250,3253,3256],{"className":3251,"style":671},[3252],"svg-align",[571,3254],{"className":3255,"style":676},[675],[571,3257,3260],{"className":3258,"style":3259},[614],"padding-left:0.833em;",[571,3261,3173],{"className":3262},[614],[571,3264,3266,3269],{"style":3265},"top:-2.8672em;",[571,3267],{"className":3268,"style":676},[675],[571,3270,3274],{"className":3271,"style":3273},[3272],"hide-tail","min-width:0.853em;height:1.08em;",[696,3275,3280],{"xmlns":698,"width":3276,"height":3277,"viewBox":3278,"preserveAspectRatio":3279},"400em","1.08em","0 0 400000 1080","xMinYMin slice",[705,3281],{"d":3282},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[571,3284,1012],{"className":3285},[1011],[571,3287,3289],{"className":3288},[664],[571,3290,3293],{"className":3291,"style":3292},[668],"height:0.1328em;",[571,3294],{},[571,3296],{"className":3297,"style":1071},[1070],[571,3299,3176],{"className":3300},[1075],[571,3302],{"className":3303,"style":1071},[1070],[571,3305,3307,3310,3313,3319],{"className":3306},[605],[571,3308],{"className":3309,"style":2993},[609],[571,3311,3123],{"className":3312},[614],[571,3314,3316],{"className":3315},[614],[571,3317,2042],{"className":3318},[2093],[571,3320,3322],{"className":3321},[614],"21",". Die Richtung ",[571,3325,3327,3349],{"className":3326},[574],[571,3328,3330],{"className":3329},[578],[580,3331,3332],{"xmlns":582},[584,3333,3334,3346],{},[587,3335,3336,3338,3340,3342,3344],{},[637,3337,819],{"stretchy":818},[852,3339,2062],{},[637,3341,2042],{"separator":601},[852,3343,2234],{},[637,3345,828],{"stretchy":818},[594,3347,3348],{"encoding":596},"(3, 4)",[571,3350,3352],{"className":3351,"ariaHidden":601},[600],[571,3353,3355,3358,3361,3364,3367,3370,3373],{"className":3354},[605],[571,3356],{"className":3357,"style":1521},[609],[571,3359,819],{"className":3360},[918],[571,3362,2062],{"className":3363},[614],[571,3365,2042],{"className":3366},[2093],[571,3368],{"className":3369,"style":1151},[1070],[571,3371,2234],{"className":3372},[614],[571,3374,828],{"className":3375},[1025]," liegt also fast in Richtung des steilsten Anstiegs.",[558,3378,3380],{"id":3379},"typische-fehler","Typische Fehler",[3382,3383,3384,3584,4931],"ul",{},[3385,3386,3387,3388,3439,3440,3515,3516,3545,3546,2013],"li",{},"Den Richtungsvektor nicht normieren. Mit ",[571,3389,3391,3412],{"className":3390},[574],[571,3392,3394],{"className":3393},[578],[580,3395,3396],{"xmlns":582},[584,3397,3398,3410],{},[587,3399,3400,3402,3404,3406,3408],{},[637,3401,819],{"stretchy":818},[852,3403,2062],{},[637,3405,2042],{"separator":601},[852,3407,2234],{},[637,3409,828],{"stretchy":818},[594,3411,3348],{"encoding":596},[571,3413,3415],{"className":3414,"ariaHidden":601},[600],[571,3416,3418,3421,3424,3427,3430,3433,3436],{"className":3417},[605],[571,3419],{"className":3420,"style":1521},[609],[571,3422,819],{"className":3423},[918],[571,3425,2062],{"className":3426},[614],[571,3428,2042],{"className":3429},[2093],[571,3431],{"className":3432,"style":1151},[1070],[571,3434,2234],{"className":3435},[614],[571,3437,828],{"className":3438},[1025]," statt ",[571,3441,3443,3467],{"className":3442},[574],[571,3444,3446],{"className":3445},[578],[580,3447,3448],{"xmlns":582},[584,3449,3450,3464],{},[587,3451,3452,3454,3456,3458,3460,3462],{},[637,3453,819],{"stretchy":818},[852,3455,2610],{},[637,3457,2613],{"separator":601},[2615,3459,2617],{},[852,3461,2620],{},[637,3463,828],{"stretchy":818},[594,3465,3466],{"encoding":596},"(0{,}6;\\ 0{,}8)",[571,3468,3470],{"className":3469,"ariaHidden":601},[600],[571,3471,3473,3476,3479,3482,3488,3491,3494,3497,3500,3503,3509,3512],{"className":3472},[605],[571,3474],{"className":3475,"style":1521},[609],[571,3477,819],{"className":3478},[918],[571,3480,854],{"className":3481},[614],[571,3483,3485],{"className":3484},[614],[571,3486,2042],{"className":3487},[2093],[571,3489,2239],{"className":3490},[614],[571,3492,2613],{"className":3493},[2093],[571,3495,2617],{"className":3496},[1070],[571,3498],{"className":3499,"style":1151},[1070],[571,3501,854],{"className":3502},[614],[571,3504,3506],{"className":3505},[614],[571,3507,2042],{"className":3508},[2093],[571,3510,2725],{"className":3511},[614],[571,3513,828],{"className":3514},[1025]," erhält man ",[571,3517,3519,3533],{"className":3518},[574],[571,3520,3522],{"className":3521},[578],[580,3523,3524],{"xmlns":582},[584,3525,3526,3531],{},[587,3527,3528],{},[852,3529,3530],{},"36",[594,3532,3530],{"encoding":596},[571,3534,3536],{"className":3535,"ariaHidden":601},[600],[571,3537,3539,3542],{"className":3538},[605],[571,3540],{"className":3541,"style":2582},[609],[571,3543,3530],{"className":3544},[614],", also das Fünffache des richtigen Werts ",[571,3547,3549,3563],{"className":3548},[574],[571,3550,3552],{"className":3551},[578],[580,3553,3554],{"xmlns":582},[584,3555,3556,3560],{},[587,3557,3558],{},[852,3559,2829],{},[594,3561,3562],{"encoding":596},"7{,}2",[571,3564,3566],{"className":3565,"ariaHidden":601},[600],[571,3567,3569,3572,3575,3581],{"className":3568},[605],[571,3570],{"className":3571,"style":2993},[609],[571,3573,3123],{"className":3574},[614],[571,3576,3578],{"className":3577},[614],[571,3579,2042],{"className":3580},[2093],[571,3582,2057],{"className":3583},[614],[3385,3585,3586,3587,3679,3680,3708,3709,3977,3978,4057,4058,4150,4151,4179,4180,4444,4445,4648,4649,4877,4878,2013],{},"Die Formel ",[571,3588,3590,3614],{"className":3589},[574],[571,3591,3593],{"className":3592},[578],[580,3594,3595],{"xmlns":582},[584,3596,3597,3611],{},[587,3598,3599,3601,3603,3605],{},[590,3600,1407],{"mathvariant":802},[590,3602,592],{},[637,3604,1412],{},[631,3606,3607,3609],{"accent":601},[590,3608,725],{},[637,3610,639],{},[594,3612,3613],{"encoding":596},"\\nabla f \\cdot \\vec v",[571,3615,3617,3638],{"className":3616,"ariaHidden":601},[600],[571,3618,3620,3623,3626,3629,3632,3635],{"className":3619},[605],[571,3621],{"className":3622,"style":610},[609],[571,3624,1407],{"className":3625},[614],[571,3627,592],{"className":3628,"style":616},[614,615],[571,3630],{"className":3631,"style":1242},[1070],[571,3633,1412],{"className":3634},[1246],[571,3636],{"className":3637,"style":1242},[1070],[571,3639,3641,3644],{"className":3640},[605],[571,3642],{"className":3643,"style":652},[609],[571,3645,3647],{"className":3646},[614,656],[571,3648,3650],{"className":3649},[660],[571,3651,3653],{"className":3652},[664],[571,3654,3656,3664],{"className":3655,"style":652},[668],[571,3657,3658,3661],{"style":671},[571,3659],{"className":3660,"style":676},[675],[571,3662,725],{"className":3663,"style":760},[614,615],[571,3665,3666,3669],{"style":671},[571,3667],{"className":3668,"style":676},[675],[571,3670,3672],{"className":3671,"style":769},[688],[571,3673,3675],{"className":3674,"style":694},[693],[696,3676,3677],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,3678],{"d":707}," verwenden, obwohl ",[571,3681,3683,3696],{"className":3682},[574],[571,3684,3686],{"className":3685},[578],[580,3687,3688],{"xmlns":582},[584,3689,3690,3694],{},[587,3691,3692],{},[590,3693,592],{},[594,3695,592],{"encoding":596},[571,3697,3699],{"className":3698,"ariaHidden":601},[600],[571,3700,3702,3705],{"className":3701},[605],[571,3703],{"className":3704,"style":610},[609],[571,3706,592],{"className":3707,"style":616},[614,615]," nicht differenzierbar ist. Ein Gegenbeispiel ist ",[571,3710,3712,3766],{"className":3711},[574],[571,3713,3715],{"className":3714},[578],[580,3716,3717],{"xmlns":582},[584,3718,3719,3763],{},[587,3720,3721,3723,3725,3727,3729,3731,3733,3735],{},[590,3722,592],{},[637,3724,819],{"stretchy":818},[590,3726,2039],{},[637,3728,2042],{"separator":601},[590,3730,2045],{},[637,3732,828],{"stretchy":818},[637,3734,831],{},[796,3736,3737,3747],{},[587,3738,3739,3745],{},[2051,3740,3741,3743],{},[590,3742,2039],{},[852,3744,2057],{},[590,3746,2045],{},[587,3748,3749,3755,3757],{},[2051,3750,3751,3753],{},[590,3752,2039],{},[852,3754,2057],{},[637,3756,871],{},[2051,3758,3759,3761],{},[590,3760,2045],{},[852,3762,2057],{},[594,3764,3765],{"encoding":596},"f(x, y) = \\frac{x^2 y}{x^2 + y^2}",[571,3767,3769,3805],{"className":3768,"ariaHidden":601},[600],[571,3770,3772,3775,3778,3781,3784,3787,3790,3793,3796,3799,3802],{"className":3771},[605],[571,3773],{"className":3774,"style":1521},[609],[571,3776,592],{"className":3777,"style":616},[614,615],[571,3779,819],{"className":3780},[918],[571,3782,2039],{"className":3783},[614,615],[571,3785,2042],{"className":3786},[2093],[571,3788],{"className":3789,"style":1151},[1070],[571,3791,2045],{"className":3792,"style":760},[614,615],[571,3794,828],{"className":3795},[1025],[571,3797],{"className":3798,"style":1071},[1070],[571,3800,831],{"className":3801},[1075],[571,3803],{"className":3804,"style":1071},[1070],[571,3806,3808,3812],{"className":3807},[605],[571,3809],{"className":3810,"style":3811},[609],"height:1.5511em;vertical-align:-0.4811em;",[571,3813,3815,3818,3974],{"className":3814},[614],[571,3816],{"className":3817},[918,919],[571,3819,3821],{"className":3820},[796],[571,3822,3824,3965],{"className":3823},[660,926],[571,3825,3827,3962],{"className":3826},[664],[571,3828,3831,3908,3916],{"className":3829,"style":3830},[668],"height:1.07em;",[571,3832,3833,3836],{"style":1890},[571,3834],{"className":3835,"style":676},[675],[571,3837,3839],{"className":3838},[1110,1111,1112,1113],[571,3840,3842,3876,3879],{"className":3841},[614,1113],[571,3843,3845,3848],{"className":3844},[614,1113],[571,3846,2039],{"className":3847},[614,615,1113],[571,3849,3851],{"className":3850},[2128],[571,3852,3854],{"className":3853},[660],[571,3855,3857],{"className":3856},[664],[571,3858,3861],{"className":3859,"style":3860},[668],"height:0.7463em;",[571,3862,3864,3868],{"style":3863},"top:-2.786em;margin-right:0.0714em;",[571,3865],{"className":3866,"style":3867},[675],"height:2.5em;",[571,3869,3873],{"className":3870},[1110,3871,3872,1113],"reset-size3","size1",[571,3874,2057],{"className":3875},[614,1113],[571,3877,871],{"className":3878},[1246,1113],[571,3880,3882,3885],{"className":3881},[614,1113],[571,3883,2045],{"className":3884,"style":760},[614,615,1113],[571,3886,3888],{"className":3887},[2128],[571,3889,3891],{"className":3890},[660],[571,3892,3894],{"className":3893},[664],[571,3895,3897],{"className":3896,"style":3860},[668],[571,3898,3899,3902],{"style":3863},[571,3900],{"className":3901,"style":3867},[675],[571,3903,3905],{"className":3904},[1110,3871,3872,1113],[571,3906,2057],{"className":3907},[614,1113],[571,3909,3910,3913],{"style":984},[571,3911],{"className":3912,"style":676},[675],[571,3914],{"className":3915,"style":992},[991],[571,3917,3919,3922],{"style":3918},"top:-3.4461em;",[571,3920],{"className":3921,"style":676},[675],[571,3923,3925],{"className":3924},[1110,1111,1112,1113],[571,3926,3928,3959],{"className":3927},[614,1113],[571,3929,3931,3934],{"className":3930},[614,1113],[571,3932,2039],{"className":3933},[614,615,1113],[571,3935,3937],{"className":3936},[2128],[571,3938,3940],{"className":3939},[660],[571,3941,3943],{"className":3942},[664],[571,3944,3947],{"className":3945,"style":3946},[668],"height:0.8913em;",[571,3948,3950,3953],{"style":3949},"top:-2.931em;margin-right:0.0714em;",[571,3951],{"className":3952,"style":3867},[675],[571,3954,3956],{"className":3955},[1110,3871,3872,1113],[571,3957,2057],{"className":3958},[614,1113],[571,3960,2045],{"className":3961,"style":760},[614,615,1113],[571,3963,1012],{"className":3964},[1011],[571,3966,3968],{"className":3967},[664],[571,3969,3972],{"className":3970,"style":3971},[668],"height:0.4811em;",[571,3973],{},[571,3975],{"className":3976},[1025,919]," mit ",[571,3979,3981,4009],{"className":3980},[574],[571,3982,3984],{"className":3983},[578],[580,3985,3986],{"xmlns":582},[584,3987,3988,4006],{},[587,3989,3990,3992,3994,3996,3998,4000,4002,4004],{},[590,3991,592],{},[637,3993,819],{"stretchy":818},[852,3995,854],{},[637,3997,2042],{"separator":601},[852,3999,854],{},[637,4001,828],{"stretchy":818},[637,4003,831],{},[852,4005,854],{},[594,4007,4008],{"encoding":596},"f(0, 0) = 0",[571,4010,4012,4048],{"className":4011,"ariaHidden":601},[600],[571,4013,4015,4018,4021,4024,4027,4030,4033,4036,4039,4042,4045],{"className":4014},[605],[571,4016],{"className":4017,"style":1521},[609],[571,4019,592],{"className":4020,"style":616},[614,615],[571,4022,819],{"className":4023},[918],[571,4025,854],{"className":4026},[614],[571,4028,2042],{"className":4029},[2093],[571,4031],{"className":4032,"style":1151},[1070],[571,4034,854],{"className":4035},[614],[571,4037,828],{"className":4038},[1025],[571,4040],{"className":4041,"style":1071},[1070],[571,4043,831],{"className":4044},[1075],[571,4046],{"className":4047,"style":1071},[1070],[571,4049,4051,4054],{"className":4050},[605],[571,4052],{"className":4053,"style":2582},[609],[571,4055,854],{"className":4056},[614],": Im Ursprung ist ",[571,4059,4061,4085],{"className":4060},[574],[571,4062,4064],{"className":4063},[578],[580,4065,4066],{"xmlns":582},[584,4067,4068,4082],{},[587,4069,4070,4072,4074,4076],{},[590,4071,1407],{"mathvariant":802},[590,4073,592],{},[637,4075,831],{},[631,4077,4078,4080],{"accent":601},[852,4079,854],{},[637,4081,639],{},[594,4083,4084],{"encoding":596},"\\nabla f = \\vec 0",[571,4086,4088,4109],{"className":4087,"ariaHidden":601},[600],[571,4089,4091,4094,4097,4100,4103,4106],{"className":4090},[605],[571,4092],{"className":4093,"style":610},[609],[571,4095,1407],{"className":4096},[614],[571,4098,592],{"className":4099,"style":616},[614,615],[571,4101],{"className":4102,"style":1071},[1070],[571,4104,831],{"className":4105},[1075],[571,4107],{"className":4108,"style":1071},[1070],[571,4110,4112,4115],{"className":4111},[605],[571,4113],{"className":4114,"style":1728},[609],[571,4116,4118],{"className":4117},[614,656],[571,4119,4121],{"className":4120},[660],[571,4122,4124],{"className":4123},[664],[571,4125,4127,4135],{"className":4126,"style":1728},[668],[571,4128,4129,4132],{"style":671},[571,4130],{"className":4131,"style":676},[675],[571,4133,854],{"className":4134},[614],[571,4136,4137,4140],{"style":1751},[571,4138],{"className":4139,"style":676},[675],[571,4141,4143],{"className":4142,"style":689},[688],[571,4144,4146],{"className":4145,"style":694},[693],[696,4147,4148],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,4149],{"d":707},", die Formel liefert also überall ",[571,4152,4154,4167],{"className":4153},[574],[571,4155,4157],{"className":4156},[578],[580,4158,4159],{"xmlns":582},[584,4160,4161,4165],{},[587,4162,4163],{},[852,4164,854],{},[594,4166,854],{"encoding":596},[571,4168,4170],{"className":4169,"ariaHidden":601},[600],[571,4171,4173,4176],{"className":4172},[605],[571,4174],{"className":4175,"style":2582},[609],[571,4177,854],{"className":4178},[614],". Die Richtungsableitung zu ",[571,4181,4183,4225],{"className":4182},[574],[571,4184,4186],{"className":4185},[578],[580,4187,4188],{"xmlns":582},[584,4189,4190,4222],{},[587,4191,4192,4198,4200,4208,4210,4212,4214,4216],{},[631,4193,4194,4196],{"accent":601},[590,4195,725],{},[637,4197,639],{},[637,4199,831],{},[796,4201,4202,4204],{},[852,4203,2225],{},[3169,4205,4206],{},[852,4207,2057],{},[637,4209,819],{"stretchy":818},[852,4211,2225],{},[637,4213,2042],{"separator":601},[852,4215,2225],{},[2051,4217,4218,4220],{},[637,4219,828],{"stretchy":818},[590,4221,2246],{},[594,4223,4224],{"encoding":596},"\\vec v = \\frac{1}{\\sqrt 2}(1, 1)^T",[571,4226,4228,4278],{"className":4227,"ariaHidden":601},[600],[571,4229,4231,4234,4269,4272,4275],{"className":4230},[605],[571,4232],{"className":4233,"style":652},[609],[571,4235,4237],{"className":4236},[614,656],[571,4238,4240],{"className":4239},[660],[571,4241,4243],{"className":4242},[664],[571,4244,4246,4254],{"className":4245,"style":652},[668],[571,4247,4248,4251],{"style":671},[571,4249],{"className":4250,"style":676},[675],[571,4252,725],{"className":4253,"style":760},[614,615],[571,4255,4256,4259],{"style":671},[571,4257],{"className":4258,"style":676},[675],[571,4260,4262],{"className":4261,"style":769},[688],[571,4263,4265],{"className":4264,"style":694},[693],[696,4266,4267],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,4268],{"d":707},[571,4270],{"className":4271,"style":1071},[1070],[571,4273,831],{"className":4274},[1075],[571,4276],{"className":4277,"style":1071},[1070],[571,4279,4281,4285,4400,4403,4406,4409,4412,4415],{"className":4280},[605],[571,4282],{"className":4283,"style":4284},[609],"height:1.3831em;vertical-align:-0.538em;",[571,4286,4288,4291,4397],{"className":4287},[614],[571,4289],{"className":4290},[918,919],[571,4292,4294],{"className":4293},[796],[571,4295,4297,4388],{"className":4296},[660,926],[571,4298,4300,4385],{"className":4299},[664],[571,4301,4304,4363,4371],{"className":4302,"style":4303},[668],"height:0.8451em;",[571,4305,4307,4310],{"style":4306},"top:-2.551em;",[571,4308],{"className":4309,"style":676},[675],[571,4311,4313],{"className":4312},[1110,1111,1112,1113],[571,4314,4316],{"className":4315},[614,1113],[571,4317,4319],{"className":4318},[614,3238,1113],[571,4320,4322,4354],{"className":4321},[660,926],[571,4323,4325,4351],{"className":4324},[664],[571,4326,4329,4338],{"className":4327,"style":4328},[668],"height:0.9128em;",[571,4330,4332,4335],{"className":4331,"style":671},[3252],[571,4333],{"className":4334,"style":676},[675],[571,4336,2057],{"className":4337,"style":3259},[614,1113],[571,4339,4341,4344],{"style":4340},"top:-2.8728em;",[571,4342],{"className":4343,"style":676},[675],[571,4345,4347],{"className":4346,"style":3273},[3272,1113],[696,4348,4349],{"xmlns":698,"width":3276,"height":3277,"viewBox":3278,"preserveAspectRatio":3279},[705,4350],{"d":3282},[571,4352,1012],{"className":4353},[1011],[571,4355,4357],{"className":4356},[664],[571,4358,4361],{"className":4359,"style":4360},[668],"height:0.1272em;",[571,4362],{},[571,4364,4365,4368],{"style":984},[571,4366],{"className":4367,"style":676},[675],[571,4369],{"className":4370,"style":992},[991],[571,4372,4373,4376],{"style":1953},[571,4374],{"className":4375,"style":676},[675],[571,4377,4379],{"className":4378},[1110,1111,1112,1113],[571,4380,4382],{"className":4381},[614,1113],[571,4383,2225],{"className":4384},[614,1113],[571,4386,1012],{"className":4387},[1011],[571,4389,4391],{"className":4390},[664],[571,4392,4395],{"className":4393,"style":4394},[668],"height:0.538em;",[571,4396],{},[571,4398],{"className":4399},[1025,919],[571,4401,819],{"className":4402},[918],[571,4404,2225],{"className":4405},[614],[571,4407,2042],{"className":4408},[2093],[571,4410],{"className":4411,"style":1151},[1070],[571,4413,2225],{"className":4414},[614],[571,4416,4418,4421],{"className":4417},[1025],[571,4419,828],{"className":4420},[1025],[571,4422,4424],{"className":4423},[2128],[571,4425,4427],{"className":4426},[660],[571,4428,4430],{"className":4429},[664],[571,4431,4433],{"className":4432,"style":2332},[668],[571,4434,4435,4438],{"style":2141},[571,4436],{"className":4437,"style":2145},[675],[571,4439,4441],{"className":4440},[1110,1111,1112,1113],[571,4442,2246],{"className":4443,"style":2344},[614,615,1113]," ist aber ",[571,4446,4448,4476],{"className":4447},[574],[571,4449,4451],{"className":4450},[578],[580,4452,4453],{"xmlns":582},[584,4454,4455,4473],{},[587,4456,4457,4469,4471],{},[796,4458,4459,4461],{},[852,4460,2225],{},[587,4462,4463,4465],{},[852,4464,2057],{},[3169,4466,4467],{},[852,4468,2057],{},[637,4470,1616],{"mathvariant":802},[852,4472,854],{},[594,4474,4475],{"encoding":596},"\\frac{1}{2\\sqrt 2} \\neq 0",[571,4477,4479,4639],{"className":4478,"ariaHidden":601},[600],[571,4480,4482,4485,4597,4600,4636],{"className":4481},[605],[571,4483],{"className":4484,"style":4284},[609],[571,4486,4488,4491,4594],{"className":4487},[614],[571,4489],{"className":4490},[918,919],[571,4492,4494],{"className":4493},[796],[571,4495,4497,4586],{"className":4496},[660,926],[571,4498,4500,4583],{"className":4499},[664],[571,4501,4503,4561,4569],{"className":4502,"style":4303},[668],[571,4504,4505,4508],{"style":4306},[571,4506],{"className":4507,"style":676},[675],[571,4509,4511],{"className":4510},[1110,1111,1112,1113],[571,4512,4514,4517],{"className":4513},[614,1113],[571,4515,2057],{"className":4516},[614,1113],[571,4518,4520],{"className":4519},[614,3238,1113],[571,4521,4523,4553],{"className":4522},[660,926],[571,4524,4526,4550],{"className":4525},[664],[571,4527,4529,4538],{"className":4528,"style":4328},[668],[571,4530,4532,4535],{"className":4531,"style":671},[3252],[571,4533],{"className":4534,"style":676},[675],[571,4536,2057],{"className":4537,"style":3259},[614,1113],[571,4539,4540,4543],{"style":4340},[571,4541],{"className":4542,"style":676},[675],[571,4544,4546],{"className":4545,"style":3273},[3272,1113],[696,4547,4548],{"xmlns":698,"width":3276,"height":3277,"viewBox":3278,"preserveAspectRatio":3279},[705,4549],{"d":3282},[571,4551,1012],{"className":4552},[1011],[571,4554,4556],{"className":4555},[664],[571,4557,4559],{"className":4558,"style":4360},[668],[571,4560],{},[571,4562,4563,4566],{"style":984},[571,4564],{"className":4565,"style":676},[675],[571,4567],{"className":4568,"style":992},[991],[571,4570,4571,4574],{"style":1953},[571,4572],{"className":4573,"style":676},[675],[571,4575,4577],{"className":4576},[1110,1111,1112,1113],[571,4578,4580],{"className":4579},[614,1113],[571,4581,2225],{"className":4582},[614,1113],[571,4584,1012],{"className":4585},[1011],[571,4587,4589],{"className":4588},[664],[571,4590,4592],{"className":4591,"style":4394},[668],[571,4593],{},[571,4595],{"className":4596},[1025,919],[571,4598],{"className":4599,"style":1071},[1070],[571,4601,4603,4630,4633],{"className":4602},[1075],[571,4604,4606],{"className":4605},[1075],[571,4607,4609],{"className":4608},[614,1685],[571,4610,4612],{"className":4611},[1689],[571,4613,4615,4618,4627],{"className":4614},[1693],[571,4616],{"className":4617,"style":610},[609],[571,4619,4621],{"className":4620},[1700],[571,4622,4624],{"className":4623},[614],[571,4625,1707],{"className":4626},[1075],[571,4628],{"className":4629},[1711],[571,4631],{"className":4632},[1070,1715],[571,4634,831],{"className":4635},[1075],[571,4637],{"className":4638,"style":1071},[1070],[571,4640,4642,4645],{"className":4641},[605],[571,4643],{"className":4644,"style":2582},[609],[571,4646,854],{"className":4647},[614],", denn ",[571,4650,4652,4692],{"className":4651},[574],[571,4653,4655],{"className":4654},[578],[580,4656,4657],{"xmlns":582},[584,4658,4659,4689],{},[587,4660,4661,4663,4665,4667,4673,4675,4677],{},[590,4662,592],{},[637,4664,819],{"stretchy":818},[590,4666,847],{},[631,4668,4669,4671],{"accent":601},[590,4670,725],{},[637,4672,639],{},[637,4674,828],{"stretchy":818},[637,4676,831],{},[796,4678,4679,4681],{},[590,4680,847],{},[587,4682,4683,4685],{},[852,4684,2057],{},[3169,4686,4687],{},[852,4688,2057],{},[594,4690,4691],{"encoding":596},"f(h \\vec v) = \\frac{h}{2\\sqrt 2}",[571,4693,4695,4757],{"className":4694,"ariaHidden":601},[600],[571,4696,4698,4701,4704,4707,4710,4745,4748,4751,4754],{"className":4697},[605],[571,4699],{"className":4700,"style":1521},[609],[571,4702,592],{"className":4703,"style":616},[614,615],[571,4705,819],{"className":4706},[918],[571,4708,847],{"className":4709},[614,615],[571,4711,4713],{"className":4712},[614,656],[571,4714,4716],{"className":4715},[660],[571,4717,4719],{"className":4718},[664],[571,4720,4722,4730],{"className":4721,"style":652},[668],[571,4723,4724,4727],{"style":671},[571,4725],{"className":4726,"style":676},[675],[571,4728,725],{"className":4729,"style":760},[614,615],[571,4731,4732,4735],{"style":671},[571,4733],{"className":4734,"style":676},[675],[571,4736,4738],{"className":4737,"style":769},[688],[571,4739,4741],{"className":4740,"style":694},[693],[696,4742,4743],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,4744],{"d":707},[571,4746,828],{"className":4747},[1025],[571,4749],{"className":4750,"style":1071},[1070],[571,4752,831],{"className":4753},[1075],[571,4755],{"className":4756,"style":1071},[1070],[571,4758,4760,4764],{"className":4759},[605],[571,4761],{"className":4762,"style":4763},[609],"height:1.4181em;vertical-align:-0.538em;",[571,4765,4767,4770,4874],{"className":4766},[614],[571,4768],{"className":4769},[918,919],[571,4771,4773],{"className":4772},[796],[571,4774,4776,4866],{"className":4775},[660,926],[571,4777,4779,4863],{"className":4778},[664],[571,4780,4783,4841,4849],{"className":4781,"style":4782},[668],"height:0.8801em;",[571,4784,4785,4788],{"style":4306},[571,4786],{"className":4787,"style":676},[675],[571,4789,4791],{"className":4790},[1110,1111,1112,1113],[571,4792,4794,4797],{"className":4793},[614,1113],[571,4795,2057],{"className":4796},[614,1113],[571,4798,4800],{"className":4799},[614,3238,1113],[571,4801,4803,4833],{"className":4802},[660,926],[571,4804,4806,4830],{"className":4805},[664],[571,4807,4809,4818],{"className":4808,"style":4328},[668],[571,4810,4812,4815],{"className":4811,"style":671},[3252],[571,4813],{"className":4814,"style":676},[675],[571,4816,2057],{"className":4817,"style":3259},[614,1113],[571,4819,4820,4823],{"style":4340},[571,4821],{"className":4822,"style":676},[675],[571,4824,4826],{"className":4825,"style":3273},[3272,1113],[696,4827,4828],{"xmlns":698,"width":3276,"height":3277,"viewBox":3278,"preserveAspectRatio":3279},[705,4829],{"d":3282},[571,4831,1012],{"className":4832},[1011],[571,4834,4836],{"className":4835},[664],[571,4837,4839],{"className":4838,"style":4360},[668],[571,4840],{},[571,4842,4843,4846],{"style":984},[571,4844],{"className":4845,"style":676},[675],[571,4847],{"className":4848,"style":992},[991],[571,4850,4851,4854],{"style":1953},[571,4852],{"className":4853,"style":676},[675],[571,4855,4857],{"className":4856},[1110,1111,1112,1113],[571,4858,4860],{"className":4859},[614,1113],[571,4861,847],{"className":4862},[614,615,1113],[571,4864,1012],{"className":4865},[1011],[571,4867,4869],{"className":4868},[664],[571,4870,4872],{"className":4871,"style":4394},[668],[571,4873],{},[571,4875],{"className":4876},[1025,919]," für ",[571,4879,4881,4900],{"className":4880},[574],[571,4882,4884],{"className":4883},[578],[580,4885,4886],{"xmlns":582},[584,4887,4888,4897],{},[587,4889,4890,4892,4895],{},[590,4891,847],{},[637,4893,4894],{},">",[852,4896,854],{},[594,4898,4899],{"encoding":596},"h > 0",[571,4901,4903,4922],{"className":4902,"ariaHidden":601},[600],[571,4904,4906,4910,4913,4916,4919],{"className":4905},[605],[571,4907],{"className":4908,"style":4909},[609],"height:0.7335em;vertical-align:-0.0391em;",[571,4911,847],{"className":4912},[614,615],[571,4914],{"className":4915,"style":1071},[1070],[571,4917,4894],{"className":4918},[1075],[571,4920],{"className":4921,"style":1071},[1070],[571,4923,4925,4928],{"className":4924},[605],[571,4926],{"className":4927,"style":2582},[609],[571,4929,854],{"className":4930},[614],[3385,4932,4933],{},"Gradient und Richtung vertauschen oder komponentenweise multiplizieren statt das Skalarprodukt zu bilden. Das Ergebnis ist eine Zahl, kein Vektor.",{"title":4935,"searchDepth":4936,"depth":4936,"links":4937},"",2,[4938,4939,4940],{"id":560,"depth":4936,"text":561},{"id":2016,"depth":4936,"text":2017},{"id":3379,"depth":4936,"text":3380},[4942,4944,4947,4949,4951,4954,4957,4959],{"lhs":4943,"rhs":2225},"sqrt(0.6^2 + 0.8^2)",{"lhs":4945,"rhs":4946},"dot([4, 6], [0.6, 0.8])","7.2",{"lhs":4948,"rhs":4946},"round(((2 + 0.6*1e-5)^2 + 3*(1 + 0.8*1e-5)^2 - ((2 - 0.6*1e-5)^2 + 3*(1 - 0.8*1e-5)^2)) \u002F (2e-5), 6)",{"lhs":4950,"rhs":854},"round(((x + cos(t)*1e-5)^2 + 3*(y + sin(t)*1e-5)^2 - ((x - cos(t)*1e-5)^2 + 3*(y - sin(t)*1e-5)^2)) \u002F (2e-5) - (2*x*cos(t) + 6*y*sin(t)), 6)",{"lhs":4952,"rhs":4953},"dot([4, 6], [4, 6] \u002F sqrt(52))","sqrt(52)",{"lhs":4955,"rhs":4956},"(1\u002Fsqrt(2))^2 * (1\u002Fsqrt(2))","sqrt(2)\u002F4",{"lhs":4958,"rhs":3530},"dot([4, 6], [3, 4])",{"lhs":4960,"rhs":4946},"36 \u002F 5","f \\text{ in } \\vec{a} \\text{ (total) differenzierbar},\\ |\\vec{v}| = 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\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\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">in\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{a}\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:0.714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">(total)\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 mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">|\\vec{v}| = 1\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\">∣\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","directional-derivative","\\frac{\\partial f}{\\partial \\vec{v}}(\\vec{a}) = \\nabla f(\\vec{a}) \\cdot \\vec{v}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" 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encoding=\"application\u002Fx-tex\">\\frac{\\partial f}{\\partial \\vec{v}}(\\vec{a}) = \\nabla f(\\vec{a}) \\cdot \\vec{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:2.0574em;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:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan 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