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ohne sie zu erreichen.",[565,1129,1130,1131,1134,1135,1312,1313,1543],{},"Für den ",[569,1132,1133],{},"Arkuskotangens"," gilt wegen ",[574,1136,1138,1177],{"className":1137},[577],[574,1139,1141],{"className":1140},[581],[583,1142,1143],{"xmlns":585},[587,1144,1145,1174],{},[590,1146,1147,1150,1153,1155,1157,1161,1163,1165,1168],{},[604,1148,1149],{},"arctan",[593,1151,1152],{},"⁡",[604,1154,867],{},[593,1156,861],{},[604,1158,1160],{"mathvariant":1159},"normal","arccot",[593,1162,1152],{},[604,1164,867],{},[593,1166,1167],{},"=",[601,1169,1170,1172],{},[604,1171,606],{},[608,1173,610],{},[624,1175,1176],{"encoding":626},"\\arctan x + \\operatorname{arccot} x = \\frac{\\pi}{2}",[574,1178,1180,1207,1238],{"className":1179,"ariaHidden":595},[631],[574,1181,1183,1187,1191,1194,1197,1201,1204],{"className":1182},[635],[574,1184],{"className":1185,"style":1186},[639],"height:0.6984em;vertical-align:-0.0833em;",[574,1188,1149],{"className":1189},[1190],"mop",[574,1192],{"className":1193,"style":759},[758],[574,1195,867],{"className":1196},[659,731],[574,1198],{"className":1199,"style":1200},[758],"margin-right:0.2222em;",[574,1202,861],{"className":1203},[919],[574,1205],{"className":1206,"style":1200},[758],[574,1208,1210,1214,1221,1224,1227,1231,1235],{"className":1209},[635],[574,1211],{"className":1212,"style":1213},[639],"height:0.6151em;",[574,1215,1217],{"className":1216},[1190],[574,1218,1160],{"className":1219},[659,1220],"mathrm",[574,1222],{"className":1223,"style":759},[758],[574,1225,867],{"className":1226},[659,731],[574,1228],{"className":1229,"style":1230},[758],"margin-right:0.2778em;",[574,1232,1167],{"className":1233},[1234],"mrel",[574,1236],{"className":1237,"style":1230},[758],[574,1239,1241,1244],{"className":1240},[635],[574,1242],{"className":1243,"style":1055},[639],[574,1245,1247,1250,1309],{"className":1246},[659],[574,1248],{"className":1249},[648,666],[574,1251,1253],{"className":1252},[601],[574,1254,1256,1301],{"className":1255},[673,674],[574,1257,1259,1298],{"className":1258},[678],[574,1260,1262,1276,1284],{"className":1261,"style":683},[682],[574,1263,1264,1267],{"style":686},[574,1265],{"className":1266,"style":691},[690],[574,1268,1270],{"className":1269},[695,696,697,698],[574,1271,1273],{"className":1272},[659,698],[574,1274,610],{"className":1275},[659,698],[574,1277,1278,1281],{"style":707},[574,1279],{"className":1280,"style":691},[690],[574,1282],{"className":1283,"style":715},[714],[574,1285,1286,1289],{"style":718},[574,1287],{"className":1288,"style":691},[690],[574,1290,1292],{"className":1291},[695,696,697,698],[574,1293,1295],{"className":1294},[659,698],[574,1296,606],{"className":1297,"style":732},[659,731,698],[574,1299,737],{"className":1300},[736],[574,1302,1304],{"className":1303},[678],[574,1305,1307],{"className":1306,"style":744},[682],[574,1308],{},[574,1310],{"className":1311},[750,666],": ",[574,1314,1316,1365],{"className":1315},[577],[574,1317,1319],{"className":1318},[581],[583,1320,1321],{"xmlns":585},[587,1322,1323,1362],{},[590,1324,1325,1328,1330,1332,1334,1342,1344,1346],{},[593,1326,596],{"stretchy":1327},"false",[604,1329,1160],{"mathvariant":1159},[593,1331,1152],{},[604,1333,867],{},[863,1335,1336,1338],{},[593,1337,622],{"stretchy":1327},[593,1339,1341],{"mathvariant":1159,"lspace":1340,"rspace":1340},"0em","′",[593,1343,1167],{},[593,1345,599],{},[601,1347,1348,1350],{},[608,1349,854],{},[590,1351,1352,1354,1356],{},[608,1353,854],{},[593,1355,861],{},[863,1357,1358,1360],{},[604,1359,867],{},[608,1361,610],{},[624,1363,1364],{"encoding":626},"(\\operatorname{arccot} x)' = -\\frac{1}{1 + x^2}",[574,1366,1368,1434],{"className":1367,"ariaHidden":595},[631],[574,1369,1371,1375,1378,1384,1387,1390,1425,1428,1431],{"className":1370},[635],[574,1372],{"className":1373,"style":1374},[639],"height:1.0019em;vertical-align:-0.25em;",[574,1376,596],{"className":1377},[648],[574,1379,1381],{"className":1380},[1190],[574,1382,1160],{"className":1383},[659,1220],[574,1385],{"className":1386,"style":759},[758],[574,1388,867],{"className":1389},[659,731],[574,1391,1393,1396],{"className":1392},[750],[574,1394,622],{"className":1395},[750],[574,1397,1399],{"className":1398},[929],[574,1400,1402],{"className":1401},[673],[574,1403,1405],{"className":1404},[678],[574,1406,1409],{"className":1407,"style":1408},[682],"height:0.7519em;",[574,1410,1412,1416],{"style":1411},"top:-3.063em;margin-right:0.05em;",[574,1413],{"className":1414,"style":1415},[690],"height:2.7em;",[574,1417,1419],{"className":1418},[695,696,697,698],[574,1420,1422],{"className":1421},[659,698],[574,1423,1341],{"className":1424},[659,698],[574,1426],{"className":1427,"style":1230},[758],[574,1429,1167],{"className":1430},[1234],[574,1432],{"className":1433,"style":1230},[758],[574,1435,1437,1440,1443],{"className":1436},[635],[574,1438],{"className":1439,"style":882},[639],[574,1441,599],{"className":1442},[659],[574,1444,1446,1449,1540],{"className":1445},[659],[574,1447],{"className":1448},[648,666],[574,1450,1452],{"className":1451},[601],[574,1453,1455,1532],{"className":1454},[673,674],[574,1456,1458,1529],{"className":1457},[678],[574,1459,1461,1507,1515],{"className":1460,"style":901},[682],[574,1462,1463,1466],{"style":686},[574,1464],{"className":1465,"style":691},[690],[574,1467,1469],{"className":1468},[695,696,697,698],[574,1470,1472,1475,1478],{"className":1471},[659,698],[574,1473,854],{"className":1474},[659,698],[574,1476,861],{"className":1477},[919,698],[574,1479,1481,1484],{"className":1480},[659,698],[574,1482,867],{"className":1483},[659,731,698],[574,1485,1487],{"className":1486},[929],[574,1488,1490],{"className":1489},[673],[574,1491,1493],{"className":1492},[678],[574,1494,1496],{"className":1495,"style":939},[682],[574,1497,1498,1501],{"style":942},[574,1499],{"className":1500,"style":946},[690],[574,1502,1504],{"className":1503},[695,950,655,698],[574,1505,610],{"className":1506},[659,698],[574,1508,1509,1512],{"style":707},[574,1510],{"className":1511,"style":691},[690],[574,1513],{"className":1514,"style":715},[714],[574,1516,1517,1520],{"style":718},[574,1518],{"className":1519,"style":691},[690],[574,1521,1523],{"className":1522},[695,696,697,698],[574,1524,1526],{"className":1525},[659,698],[574,1527,854],{"className":1528},[659,698],[574,1530,737],{"className":1531},[736],[574,1533,1535],{"className":1534},[678],[574,1536,1538],{"className":1537,"style":985},[682],[574,1539],{},[574,1541],{"className":1542},[750,666],".",[565,1545,1546,1547,1586,1587,1726],{},"Die Formel ist vor allem rückwärts wichtig: ",[574,1548,1550,1568],{"className":1549},[577],[574,1551,1553],{"className":1552},[581],[583,1554,1555],{"xmlns":585},[587,1556,1557,1565],{},[590,1558,1559,1561,1563],{},[604,1560,1149],{},[593,1562,1152],{},[604,1564,867],{},[624,1566,1567],{"encoding":626},"\\arctan x",[574,1569,1571],{"className":1570,"ariaHidden":595},[631],[574,1572,1574,1577,1580,1583],{"className":1573},[635],[574,1575],{"className":1576,"style":1213},[639],[574,1578,1149],{"className":1579},[1190],[574,1581],{"className":1582,"style":759},[758],[574,1584,867],{"className":1585},[659,731]," ist eine Stammfunktion von ",[574,1588,1590,1617],{"className":1589},[577],[574,1591,1593],{"className":1592},[581],[583,1594,1595],{"xmlns":585},[587,1596,1597,1615],{},[590,1598,1599],{},[601,1600,1601,1603],{},[608,1602,854],{},[590,1604,1605,1607,1609],{},[608,1606,854],{},[593,1608,861],{},[863,1610,1611,1613],{},[604,1612,867],{},[608,1614,610],{},[624,1616,872],{"encoding":626},[574,1618,1620],{"className":1619,"ariaHidden":595},[631],[574,1621,1623,1626],{"className":1622},[635],[574,1624],{"className":1625,"style":882},[639],[574,1627,1629,1632,1723],{"className":1628},[659],[574,1630],{"className":1631},[648,666],[574,1633,1635],{"className":1634},[601],[574,1636,1638,1715],{"className":1637},[673,674],[574,1639,1641,1712],{"className":1640},[678],[574,1642,1644,1690,1698],{"className":1643,"style":901},[682],[574,1645,1646,1649],{"style":686},[574,1647],{"className":1648,"style":691},[690],[574,1650,1652],{"className":1651},[695,696,697,698],[574,1653,1655,1658,1661],{"className":1654},[659,698],[574,1656,854],{"className":1657},[659,698],[574,1659,861],{"className":1660},[919,698],[574,1662,1664,1667],{"className":1663},[659,698],[574,1665,867],{"className":1666},[659,731,698],[574,1668,1670],{"className":1669},[929],[574,1671,1673],{"className":1672},[673],[574,1674,1676],{"className":1675},[678],[574,1677,1679],{"className":1678,"style":939},[682],[574,1680,1681,1684],{"style":942},[574,1682],{"className":1683,"style":946},[690],[574,1685,1687],{"className":1686},[695,950,655,698],[574,1688,610],{"className":1689},[659,698],[574,1691,1692,1695],{"style":707},[574,1693],{"className":1694,"style":691},[690],[574,1696],{"className":1697,"style":715},[714],[574,1699,1700,1703],{"style":718},[574,1701],{"className":1702,"style":691},[690],[574,1704,1706],{"className":1705},[695,696,697,698],[574,1707,1709],{"className":1708},[659,698],[574,1710,854],{"className":1711},[659,698],[574,1713,737],{"className":1714},[736],[574,1716,1718],{"className":1717},[678],[574,1719,1721],{"className":1720,"style":985},[682],[574,1722],{},[574,1724],{"className":1725},[750,666],", einer rationalen Funktion ohne Nullstellen im Nenner.",[560,1728,1730],{"id":1729},"herleitung","Herleitung",[565,1732,1733,1734,1797,1798,1862,1863,1960],{},"Mit der Ableitung der Umkehrfunktion und ",[574,1735,1737,1760],{"className":1736},[577],[574,1738,1740],{"className":1739},[581],[583,1741,1742],{"xmlns":585},[587,1743,1744,1757],{},[590,1745,1746,1749,1751,1753,1755],{},[604,1747,1748],{},"y",[593,1750,1167],{},[604,1752,1149],{},[593,1754,1152],{},[604,1756,867],{},[624,1758,1759],{"encoding":626},"y = \\arctan x",[574,1761,1763,1782],{"className":1762,"ariaHidden":595},[631],[574,1764,1766,1770,1773,1776,1779],{"className":1765},[635],[574,1767],{"className":1768,"style":1769},[639],"height:0.625em;vertical-align:-0.1944em;",[574,1771,1748],{"className":1772,"style":732},[659,731],[574,1774],{"className":1775,"style":1230},[758],[574,1777,1167],{"className":1778},[1234],[574,1780],{"className":1781,"style":1230},[758],[574,1783,1785,1788,1791,1794],{"className":1784},[635],[574,1786],{"className":1787,"style":1213},[639],[574,1789,1149],{"className":1790},[1190],[574,1792],{"className":1793,"style":759},[758],[574,1795,867],{"className":1796},[659,731],", also ",[574,1799,1801,1824],{"className":1800},[577],[574,1802,1804],{"className":1803},[581],[583,1805,1806],{"xmlns":585},[587,1807,1808,1821],{},[590,1809,1810,1813,1815,1817,1819],{},[604,1811,1812],{},"tan",[593,1814,1152],{},[604,1816,1748],{},[593,1818,1167],{},[604,1820,867],{},[624,1822,1823],{"encoding":626},"\\tan y = x",[574,1825,1827,1852],{"className":1826,"ariaHidden":595},[631],[574,1828,1830,1834,1837,1840,1843,1846,1849],{"className":1829},[635],[574,1831],{"className":1832,"style":1833},[639],"height:0.8095em;vertical-align:-0.1944em;",[574,1835,1812],{"className":1836},[1190],[574,1838],{"className":1839,"style":759},[758],[574,1841,1748],{"className":1842,"style":732},[659,731],[574,1844],{"className":1845,"style":1230},[758],[574,1847,1167],{"className":1848},[1234],[574,1850],{"className":1851,"style":1230},[758],[574,1853,1855,1859],{"className":1854},[635],[574,1856],{"className":1857,"style":1858},[639],"height:0.4306em;",[574,1860,867],{"className":1861},[659,731],". Die Ableitung des Tangens schreibt man als ",[574,1864,1866,1894],{"className":1865},[577],[574,1867,1869],{"className":1868},[581],[583,1870,1871],{"xmlns":585},[587,1872,1873,1891],{},[590,1874,1875,1877,1879,1889],{},[608,1876,854],{},[593,1878,861],{},[863,1880,1881,1887],{},[590,1882,1883,1885],{},[604,1884,1812],{},[593,1886,1152],{},[608,1888,610],{},[604,1890,1748],{},[624,1892,1893],{"encoding":626},"1 + \\tan^2 y",[574,1895,1897,1916],{"className":1896,"ariaHidden":595},[631],[574,1898,1900,1904,1907,1910,1913],{"className":1899},[635],[574,1901],{"className":1902,"style":1903},[639],"height:0.7278em;vertical-align:-0.0833em;",[574,1905,854],{"className":1906},[659],[574,1908],{"className":1909,"style":1200},[758],[574,1911,861],{"className":1912},[919],[574,1914],{"className":1915,"style":1200},[758],[574,1917,1919,1923,1954,1957],{"className":1918},[635],[574,1920],{"className":1921,"style":1922},[639],"height:1.0135em;vertical-align:-0.1944em;",[574,1924,1926,1929],{"className":1925},[1190],[574,1927,1812],{"className":1928},[1190],[574,1930,1932],{"className":1931},[929],[574,1933,1935],{"className":1934},[673],[574,1936,1938],{"className":1937},[678],[574,1939,1942],{"className":1940,"style":1941},[682],"height:0.8191em;",[574,1943,1945,1948],{"style":1944},"top:-3.068em;margin-right:0.05em;",[574,1946],{"className":1947,"style":1415},[690],[574,1949,1951],{"className":1950},[695,696,697,698],[574,1952,610],{"className":1953},[659,698],[574,1955],{"className":1956,"style":759},[758],[574,1958,1748],{"className":1959,"style":732},[659,731],":",[574,1962,1965],{"className":1963},[1964],"katex-display",[574,1966,1968,2037],{"className":1967},[577],[574,1969,1971],{"className":1970},[581],[583,1972,1974],{"xmlns":585,"display":1973},"block",[587,1975,1976,2034],{},[590,1977,1978,1980,1982,1984,1986,1992,1994,2016,2018],{},[593,1979,596],{"stretchy":1327},[604,1981,1149],{},[593,1983,1152],{},[604,1985,867],{},[863,1987,1988,1990],{},[593,1989,622],{"stretchy":1327},[593,1991,1341],{"mathvariant":1159,"lspace":1340,"rspace":1340},[593,1993,1167],{},[601,1995,1996,1998],{},[608,1997,854],{},[590,1999,2000,2002,2004,2014],{},[608,2001,854],{},[593,2003,861],{},[863,2005,2006,2012],{},[590,2007,2008,2010],{},[604,2009,1812],{},[593,2011,1152],{},[608,2013,610],{},[604,2015,1748],{},[593,2017,1167],{},[601,2019,2020,2022],{},[608,2021,854],{},[590,2023,2024,2026,2028],{},[608,2025,854],{},[593,2027,861],{},[863,2029,2030,2032],{},[604,2031,867],{},[608,2033,610],{},[624,2035,2036],{"encoding":626},"(\\arctan x)' = \\frac{1}{1 + \\tan^2 y} = \\frac{1}{1 + x^2}",[574,2038,2040,2102,2228],{"className":2039,"ariaHidden":595},[631],[574,2041,2043,2047,2050,2053,2056,2059,2093,2096,2099],{"className":2042},[635],[574,2044],{"className":2045,"style":2046},[639],"height:1.0519em;vertical-align:-0.25em;",[574,2048,596],{"className":2049},[648],[574,2051,1149],{"className":2052},[1190],[574,2054],{"className":2055,"style":759},[758],[574,2057,867],{"className":2058},[659,731],[574,2060,2062,2065],{"className":2061},[750],[574,2063,622],{"className":2064},[750],[574,2066,2068],{"className":2067},[929],[574,2069,2071],{"className":2070},[673],[574,2072,2074],{"className":2073},[678],[574,2075,2078],{"className":2076,"style":2077},[682],"height:0.8019em;",[574,2079,2081,2084],{"style":2080},"top:-3.113em;margin-right:0.05em;",[574,2082],{"className":2083,"style":1415},[690],[574,2085,2087],{"className":2086},[695,696,697,698],[574,2088,2090],{"className":2089},[659,698],[574,2091,1341],{"className":2092},[659,698],[574,2094],{"className":2095,"style":1230},[758],[574,2097,1167],{"className":2098},[1234],[574,2100],{"className":2101,"style":1230},[758],[574,2103,2105,2109,2219,2222,2225],{"className":2104},[635],[574,2106],{"className":2107,"style":2108},[639],"height:2.225em;vertical-align:-0.9035em;",[574,2110,2112,2115,2216],{"className":2111},[659],[574,2113],{"className":2114},[648,666],[574,2116,2118],{"className":2117},[601],[574,2119,2121,2207],{"className":2120},[673,674],[574,2122,2124,2204],{"className":2123},[678],[574,2125,2128,2184,2192],{"className":2126,"style":2127},[682],"height:1.3214em;",[574,2129,2131,2134],{"style":2130},"top:-2.2909em;",[574,2132],{"className":2133,"style":691},[690],[574,2135,2137,2140,2143,2146,2149,2178,2181],{"className":2136},[659],[574,2138,854],{"className":2139},[659],[574,2141],{"className":2142,"style":1200},[758],[574,2144,861],{"className":2145},[919],[574,2147],{"className":2148,"style":1200},[758],[574,2150,2152,2155],{"className":2151},[1190],[574,2153,1812],{"className":2154},[1190],[574,2156,2158],{"className":2157},[929],[574,2159,2161],{"className":2160},[673],[574,2162,2164],{"className":2163},[678],[574,2165,2167],{"className":2166,"style":1941},[682],[574,2168,2169,2172],{"style":1944},[574,2170],{"className":2171,"style":1415},[690],[574,2173,2175],{"className":2174},[695,696,697,698],[574,2176,610],{"className":2177},[659,698],[574,2179],{"className":2180,"style":759},[758],[574,2182,1748],{"className":2183,"style":732},[659,731],[574,2185,2186,2189],{"style":707},[574,2187],{"className":2188,"style":691},[690],[574,2190],{"className":2191,"style":715},[714],[574,2193,2195,2198],{"style":2194},"top:-3.677em;",[574,2196],{"className":2197,"style":691},[690],[574,2199,2201],{"className":2200},[659],[574,2202,854],{"className":2203},[659],[574,2205,737],{"className":2206},[736],[574,2208,2210],{"className":2209},[678],[574,2211,2214],{"className":2212,"style":2213},[682],"height:0.9035em;",[574,2215],{},[574,2217],{"className":2218},[750,666],[574,2220],{"className":2221,"style":1230},[758],[574,2223,1167],{"className":2224},[1234],[574,2226],{"className":2227,"style":1230},[758],[574,2229,2231,2235],{"className":2230},[635],[574,2232],{"className":2233,"style":2234},[639],"height:2.0908em;vertical-align:-0.7693em;",[574,2236,2238,2241,2336],{"className":2237},[659],[574,2239],{"className":2240},[648,666],[574,2242,2244],{"className":2243},[601],[574,2245,2247,2327],{"className":2246},[673,674],[574,2248,2250,2324],{"className":2249},[678],[574,2251,2253,2305,2313],{"className":2252,"style":2127},[682],[574,2254,2256,2259],{"style":2255},"top:-2.314em;",[574,2257],{"className":2258,"style":691},[690],[574,2260,2262,2265,2268,2271,2274],{"className":2261},[659],[574,2263,854],{"className":2264},[659],[574,2266],{"className":2267,"style":1200},[758],[574,2269,861],{"className":2270},[919],[574,2272],{"className":2273,"style":1200},[758],[574,2275,2277,2280],{"className":2276},[659],[574,2278,867],{"className":2279},[659,731],[574,2281,2283],{"className":2282},[929],[574,2284,2286],{"className":2285},[673],[574,2287,2289],{"className":2288},[678],[574,2290,2293],{"className":2291,"style":2292},[682],"height:0.7401em;",[574,2294,2296,2299],{"style":2295},"top:-2.989em;margin-right:0.05em;",[574,2297],{"className":2298,"style":1415},[690],[574,2300,2302],{"className":2301},[695,696,697,698],[574,2303,610],{"className":2304},[659,698],[574,2306,2307,2310],{"style":707},[574,2308],{"className":2309,"style":691},[690],[574,2311],{"className":2312,"style":715},[714],[574,2314,2315,2318],{"style":2194},[574,2316],{"className":2317,"style":691},[690],[574,2319,2321],{"className":2320},[659],[574,2322,854],{"className":2323},[659],[574,2325,737],{"className":2326},[736],[574,2328,2330],{"className":2329},[678],[574,2331,2334],{"className":2332,"style":2333},[682],"height:0.7693em;",[574,2335],{},[574,2337],{"className":2338},[750,666],[560,2340,2342],{"id":2341},"beispiele","Beispiele",[565,2344,2345,2346,2398,2399,1960],{},"An den Stellen ",[574,2347,2349,2368],{"className":2348},[577],[574,2350,2352],{"className":2351},[581],[583,2353,2354],{"xmlns":585},[587,2355,2356,2365],{},[590,2357,2358,2360,2362],{},[604,2359,867],{},[593,2361,1167],{},[608,2363,2364],{},"0",[624,2366,2367],{"encoding":626},"x = 0",[574,2369,2371,2389],{"className":2370,"ariaHidden":595},[631],[574,2372,2374,2377,2380,2383,2386],{"className":2373},[635],[574,2375],{"className":2376,"style":1858},[639],[574,2378,867],{"className":2379},[659,731],[574,2381],{"className":2382,"style":1230},[758],[574,2384,1167],{"className":2385},[1234],[574,2387],{"className":2388,"style":1230},[758],[574,2390,2392,2395],{"className":2391},[635],[574,2393],{"className":2394,"style":1017},[639],[574,2396,2364],{"className":2397},[659]," und ",[574,2400,2402,2420],{"className":2401},[577],[574,2403,2405],{"className":2404},[581],[583,2406,2407],{"xmlns":585},[587,2408,2409,2417],{},[590,2410,2411,2413,2415],{},[604,2412,867],{},[593,2414,1167],{},[608,2416,854],{},[624,2418,2419],{"encoding":626},"x = 1",[574,2421,2423,2441],{"className":2422,"ariaHidden":595},[631],[574,2424,2426,2429,2432,2435,2438],{"className":2425},[635],[574,2427],{"className":2428,"style":1858},[639],[574,2430,867],{"className":2431},[659,731],[574,2433],{"className":2434,"style":1230},[758],[574,2436,1167],{"className":2437},[1234],[574,2439],{"className":2440,"style":1230},[758],[574,2442,2444,2447],{"className":2443},[635],[574,2445],{"className":2446,"style":1017},[639],[574,2448,854],{"className":2449},[659],[574,2451,2453],{"className":2452},[1964],[574,2454,2456,2538],{"className":2455},[577],[574,2457,2459],{"className":2458},[581],[583,2460,2461],{"xmlns":585,"display":1973},[587,2462,2463,2535],{},[590,2464,2465,2472,2474,2476,2478,2480,2492,2494,2496,2498,2501,2507,2509,2511,2513,2515,2527,2529],{},[863,2466,2467,2470],{},[604,2468,2469],{},"f",[593,2471,1341],{"mathvariant":1159,"lspace":1340,"rspace":1340},[593,2473,596],{"stretchy":1327},[608,2475,2364],{},[593,2477,622],{"stretchy":1327},[593,2479,1167],{},[601,2481,2482,2484],{},[608,2483,854],{},[590,2485,2486,2488,2490],{},[608,2487,854],{},[593,2489,861],{},[608,2491,2364],{},[593,2493,1167],{},[608,2495,854],{},[593,2497,613],{"separator":595},[758,2499],{"width":2500},"2em",[863,2502,2503,2505],{},[604,2504,2469],{},[593,2506,1341],{"mathvariant":1159,"lspace":1340,"rspace":1340},[593,2508,596],{"stretchy":1327},[608,2510,854],{},[593,2512,622],{"stretchy":1327},[593,2514,1167],{},[601,2516,2517,2519],{},[608,2518,854],{},[590,2520,2521,2523,2525],{},[608,2522,854],{},[593,2524,861],{},[608,2526,854],{},[593,2528,1167],{},[601,2530,2531,2533],{},[608,2532,854],{},[608,2534,610],{},[624,2536,2537],{"encoding":626},"f'(0) = \\frac{1}{1 + 0} = 1, \\qquad f'(1) = \\frac{1}{1 + 1} = \\frac{1}{2}",[574,2539,2541,2598,2687,2756,2845],{"className":2540,"ariaHidden":595},[631],[574,2542,2544,2547,2580,2583,2586,2589,2592,2595],{"className":2543},[635],[574,2545],{"className":2546,"style":2046},[639],[574,2548,2550,2554],{"className":2549},[659],[574,2551,2469],{"className":2552,"style":2553},[659,731],"margin-right:0.1076em;",[574,2555,2557],{"className":2556},[929],[574,2558,2560],{"className":2559},[673],[574,2561,2563],{"className":2562},[678],[574,2564,2566],{"className":2565,"style":2077},[682],[574,2567,2568,2571],{"style":2080},[574,2569],{"className":2570,"style":1415},[690],[574,2572,2574],{"className":2573},[695,696,697,698],[574,2575,2577],{"className":2576},[659,698],[574,2578,1341],{"className":2579},[659,698],[574,2581,596],{"className":2582},[648],[574,2584,2364],{"className":2585},[659],[574,2587,622],{"className":2588},[750],[574,2590],{"className":2591,"style":1230},[758],[574,2593,1167],{"className":2594},[1234],[574,2596],{"className":2597,"style":1230},[758],[574,2599,2601,2604,2678,2681,2684],{"className":2600},[635],[574,2602],{"className":2603,"style":2234},[639],[574,2605,2607,2610,2675],{"className":2606},[659],[574,2608],{"className":2609},[648,666],[574,2611,2613],{"className":2612},[601],[574,2614,2616,2667],{"className":2615},[673,674],[574,2617,2619,2664],{"className":2618},[678],[574,2620,2622,2645,2653],{"className":2621,"style":2127},[682],[574,2623,2624,2627],{"style":2255},[574,2625],{"className":2626,"style":691},[690],[574,2628,2630,2633,2636,2639,2642],{"className":2629},[659],[574,2631,854],{"className":2632},[659],[574,2634],{"className":2635,"style":1200},[758],[574,2637,861],{"className":2638},[919],[574,2640],{"className":2641,"style":1200},[758],[574,2643,2364],{"className":2644},[659],[574,2646,2647,2650],{"style":707},[574,2648],{"className":2649,"style":691},[690],[574,2651],{"className":2652,"style":715},[714],[574,2654,2655,2658],{"style":2194},[574,2656],{"className":2657,"style":691},[690],[574,2659,2661],{"className":2660},[659],[574,2662,854],{"className":2663},[659],[574,2665,737],{"className":2666},[736],[574,2668,2670],{"className":2669},[678],[574,2671,2673],{"className":2672,"style":2333},[682],[574,2674],{},[574,2676],{"className":2677},[750,666],[574,2679],{"className":2680,"style":1230},[758],[574,2682,1167],{"className":2683},[1234],[574,2685],{"className":2686,"style":1230},[758],[574,2688,2690,2693,2696,2699,2703,2706,2738,2741,2744,2747,2750,2753],{"className":2689},[635],[574,2691],{"className":2692,"style":2046},[639],[574,2694,854],{"className":2695},[659],[574,2697,613],{"className":2698},[754],[574,2700],{"className":2701,"style":2702},[758],"margin-right:2em;",[574,2704],{"className":2705,"style":759},[758],[574,2707,2709,2712],{"className":2708},[659],[574,2710,2469],{"className":2711,"style":2553},[659,731],[574,2713,2715],{"className":2714},[929],[574,2716,2718],{"className":2717},[673],[574,2719,2721],{"className":2720},[678],[574,2722,2724],{"className":2723,"style":2077},[682],[574,2725,2726,2729],{"style":2080},[574,2727],{"className":2728,"style":1415},[690],[574,2730,2732],{"className":2731},[695,696,697,698],[574,2733,2735],{"className":2734},[659,698],[574,2736,1341],{"className":2737},[659,698],[574,2739,596],{"className":2740},[648],[574,2742,854],{"className":2743},[659],[574,2745,622],{"className":2746},[750],[574,2748],{"className":2749,"style":1230},[758],[574,2751,1167],{"className":2752},[1234],[574,2754],{"className":2755,"style":1230},[758],[574,2757,2759,2762,2836,2839,2842],{"className":2758},[635],[574,2760],{"className":2761,"style":2234},[639],[574,2763,2765,2768,2833],{"className":2764},[659],[574,2766],{"className":2767},[648,666],[574,2769,2771],{"className":2770},[601],[574,2772,2774,2825],{"className":2773},[673,674],[574,2775,2777,2822],{"className":2776},[678],[574,2778,2780,2803,2811],{"className":2779,"style":2127},[682],[574,2781,2782,2785],{"style":2255},[574,2783],{"className":2784,"style":691},[690],[574,2786,2788,2791,2794,2797,2800],{"className":2787},[659],[574,2789,854],{"className":2790},[659],[574,2792],{"className":2793,"style":1200},[758],[574,2795,861],{"className":2796},[919],[574,2798],{"className":2799,"style":1200},[758],[574,2801,854],{"className":2802},[659],[574,2804,2805,2808],{"style":707},[574,2806],{"className":2807,"style":691},[690],[574,2809],{"className":2810,"style":715},[714],[574,2812,2813,2816],{"style":2194},[574,2814],{"className":2815,"style":691},[690],[574,2817,2819],{"className":2818},[659],[574,2820,854],{"className":2821},[659],[574,2823,737],{"className":2824},[736],[574,2826,2828],{"className":2827},[678],[574,2829,2831],{"className":2830,"style":2333},[682],[574,2832],{},[574,2834],{"className":2835},[750,666],[574,2837],{"className":2838,"style":1230},[758],[574,2840,1167],{"className":2841},[1234],[574,2843],{"className":2844,"style":1230},[758],[574,2846,2848,2852],{"className":2847},[635],[574,2849],{"className":2850,"style":2851},[639],"height:2.0074em;vertical-align:-0.686em;",[574,2853,2855,2858,2912],{"className":2854},[659],[574,2856],{"className":2857},[648,666],[574,2859,2861],{"className":2860},[601],[574,2862,2864,2903],{"className":2863},[673,674],[574,2865,2867,2900],{"className":2866},[678],[574,2868,2870,2881,2889],{"className":2869,"style":2127},[682],[574,2871,2872,2875],{"style":2255},[574,2873],{"className":2874,"style":691},[690],[574,2876,2878],{"className":2877},[659],[574,2879,610],{"className":2880},[659],[574,2882,2883,2886],{"style":707},[574,2884],{"className":2885,"style":691},[690],[574,2887],{"className":2888,"style":715},[714],[574,2890,2891,2894],{"style":2194},[574,2892],{"className":2893,"style":691},[690],[574,2895,2897],{"className":2896},[659],[574,2898,854],{"className":2899},[659],[574,2901,737],{"className":2902},[736],[574,2904,2906],{"className":2905},[678],[574,2907,2910],{"className":2908,"style":2909},[682],"height:0.686em;",[574,2911],{},[574,2913],{"className":2914},[750,666],[565,2916,2917,2918,1960],{},"Mit der Kettenregel, innere Funktion ",[574,2919,2921,2939],{"className":2920},[577],[574,2922,2924],{"className":2923},[581],[583,2925,2926],{"xmlns":585},[587,2927,2928,2936],{},[590,2929,2930],{},[863,2931,2932,2934],{},[604,2933,867],{},[608,2935,610],{},[624,2937,2938],{"encoding":626},"x^2",[574,2940,2942],{"className":2941,"ariaHidden":595},[631],[574,2943,2945,2949],{"className":2944},[635],[574,2946],{"className":2947,"style":2948},[639],"height:0.8141em;",[574,2950,2952,2955],{"className":2951},[659],[574,2953,867],{"className":2954},[659,731],[574,2956,2958],{"className":2957},[929],[574,2959,2961],{"className":2960},[673],[574,2962,2964],{"className":2963},[678],[574,2965,2967],{"className":2966,"style":2948},[682],[574,2968,2969,2972],{"style":1411},[574,2970],{"className":2971,"style":1415},[690],[574,2973,2975],{"className":2974},[695,696,697,698],[574,2976,610],{"className":2977},[659,698],[574,2979,2981],{"className":2980},[1964],[574,2982,2984,3093],{"className":2983},[577],[574,2985,2987],{"className":2986},[581],[583,2988,2989],{"xmlns":585,"display":1973},[587,2990,2991,3090],{},[590,2992,2993,2996,2998,3000,3002,3004,3006,3008,3010,3016,3018,3022,3025,3027,3033,3035,3037,3039,3041,3062,3064,3066,3072,3074,3076,3078,3080,3086,3088],{},[604,2994,2995],{},"g",[593,2997,596],{"stretchy":1327},[604,2999,867],{},[593,3001,622],{"stretchy":1327},[593,3003,1167],{},[604,3005,1149],{},[593,3007,1152],{},[593,3009,596],{"stretchy":1327},[863,3011,3012,3014],{},[604,3013,867],{},[608,3015,610],{},[593,3017,622],{"stretchy":1327},[3019,3020,3021],"mtext",{},"  ",[593,3023,3024],{},"⇒",[3019,3026,3021],{},[863,3028,3029,3031],{},[604,3030,2995],{},[593,3032,1341],{"mathvariant":1159,"lspace":1340,"rspace":1340},[593,3034,596],{"stretchy":1327},[604,3036,867],{},[593,3038,622],{"stretchy":1327},[593,3040,1167],{},[601,3042,3043,3049],{},[590,3044,3045,3047],{},[608,3046,610],{},[604,3048,867],{},[590,3050,3051,3053,3055],{},[608,3052,854],{},[593,3054,861],{},[863,3056,3057,3059],{},[604,3058,867],{},[608,3060,3061],{},"4",[593,3063,613],{"separator":595},[758,3065],{"width":2500},[863,3067,3068,3070],{},[604,3069,2995],{},[593,3071,1341],{"mathvariant":1159,"lspace":1340,"rspace":1340},[593,3073,596],{"stretchy":1327},[608,3075,854],{},[593,3077,622],{"stretchy":1327},[593,3079,1167],{},[601,3081,3082,3084],{},[608,3083,610],{},[608,3085,610],{},[593,3087,1167],{},[608,3089,854],{},[624,3091,3092],{"encoding":626},"g(x) = \\arctan(x^2) \\;\\Rightarrow\\; g'(x) = \\frac{2x}{1 + x^4}, \\qquad g'(1) = \\frac{2}{2} = 1",[574,3094,3096,3124,3185,3241,3409,3486],{"className":3095,"ariaHidden":595},[631],[574,3097,3099,3103,3106,3109,3112,3115,3118,3121],{"className":3098},[635],[574,3100],{"className":3101,"style":3102},[639],"height:1em;vertical-align:-0.25em;",[574,3104,2995],{"className":3105,"style":732},[659,731],[574,3107,596],{"className":3108},[648],[574,3110,867],{"className":3111},[659,731],[574,3113,622],{"className":3114},[750],[574,3116],{"className":3117,"style":1230},[758],[574,3119,1167],{"className":3120},[1234],[574,3122],{"className":3123,"style":1230},[758],[574,3125,3127,3131,3134,3137,3167,3170,3173,3176,3179,3182],{"className":3126},[635],[574,3128],{"className":3129,"style":3130},[639],"height:1.1141em;vertical-align:-0.25em;",[574,3132,1149],{"className":3133},[1190],[574,3135,596],{"className":3136},[648],[574,3138,3140,3143],{"className":3139},[659],[574,3141,867],{"className":3142},[659,731],[574,3144,3146],{"className":3145},[929],[574,3147,3149],{"className":3148},[673],[574,3150,3152],{"className":3151},[678],[574,3153,3156],{"className":3154,"style":3155},[682],"height:0.8641em;",[574,3157,3158,3161],{"style":2080},[574,3159],{"className":3160,"style":1415},[690],[574,3162,3164],{"className":3163},[695,696,697,698],[574,3165,610],{"className":3166},[659,698],[574,3168,622],{"className":3169},[750],[574,3171],{"className":3172,"style":1230},[758],[574,3174],{"className":3175,"style":1230},[758],[574,3177,3024],{"className":3178},[1234],[574,3180],{"className":3181,"style":1230},[758],[574,3183],{"className":3184,"style":1230},[758],[574,3186,3188,3191,3223,3226,3229,3232,3235,3238],{"className":3187},[635],[574,3189],{"className":3190,"style":2046},[639],[574,3192,3194,3197],{"className":3193},[659],[574,3195,2995],{"className":3196,"style":732},[659,731],[574,3198,3200],{"className":3199},[929],[574,3201,3203],{"className":3202},[673],[574,3204,3206],{"className":3205},[678],[574,3207,3209],{"className":3208,"style":2077},[682],[574,3210,3211,3214],{"style":2080},[574,3212],{"className":3213,"style":1415},[690],[574,3215,3217],{"className":3216},[695,696,697,698],[574,3218,3220],{"className":3219},[659,698],[574,3221,1341],{"className":3222},[659,698],[574,3224,596],{"className":3225},[648],[574,3227,867],{"className":3228},[659,731],[574,3230,622],{"className":3231},[750],[574,3233],{"className":3234,"style":1230},[758],[574,3236,1167],{"className":3237},[1234],[574,3239],{"className":3240,"style":1230},[758],[574,3242,3244,3247,3350,3353,3356,3359,3391,3394,3397,3400,3403,3406],{"className":3243},[635],[574,3245],{"className":3246,"style":2234},[639],[574,3248,3250,3253,3347],{"className":3249},[659],[574,3251],{"className":3252},[648,666],[574,3254,3256],{"className":3255},[601],[574,3257,3259,3339],{"className":3258},[673,674],[574,3260,3262,3336],{"className":3261},[678],[574,3263,3265,3314,3322],{"className":3264,"style":2127},[682],[574,3266,3267,3270],{"style":2255},[574,3268],{"className":3269,"style":691},[690],[574,3271,3273,3276,3279,3282,3285],{"className":3272},[659],[574,3274,854],{"className":3275},[659],[574,3277],{"className":3278,"style":1200},[758],[574,3280,861],{"className":3281},[919],[574,3283],{"className":3284,"style":1200},[758],[574,3286,3288,3291],{"className":3287},[659],[574,3289,867],{"className":3290},[659,731],[574,3292,3294],{"className":3293},[929],[574,3295,3297],{"className":3296},[673],[574,3298,3300],{"className":3299},[678],[574,3301,3303],{"className":3302,"style":2292},[682],[574,3304,3305,3308],{"style":2295},[574,3306],{"className":3307,"style":1415},[690],[574,3309,3311],{"className":3310},[695,696,697,698],[574,3312,3061],{"className":3313},[659,698],[574,3315,3316,3319],{"style":707},[574,3317],{"className":3318,"style":691},[690],[574,3320],{"className":3321,"style":715},[714],[574,3323,3324,3327],{"style":2194},[574,3325],{"className":3326,"style":691},[690],[574,3328,3330,3333],{"className":3329},[659],[574,3331,610],{"className":3332},[659],[574,3334,867],{"className":3335},[659,731],[574,3337,737],{"className":3338},[736],[574,3340,3342],{"className":3341},[678],[574,3343,3345],{"className":3344,"style":2333},[682],[574,3346],{},[574,3348],{"className":3349},[750,666],[574,3351,613],{"className":3352},[754],[574,3354],{"className":3355,"style":2702},[758],[574,3357],{"className":3358,"style":759},[758],[574,3360,3362,3365],{"className":3361},[659],[574,3363,2995],{"className":3364,"style":732},[659,731],[574,3366,3368],{"className":3367},[929],[574,3369,3371],{"className":3370},[673],[574,3372,3374],{"className":3373},[678],[574,3375,3377],{"className":3376,"style":2077},[682],[574,3378,3379,3382],{"style":2080},[574,3380],{"className":3381,"style":1415},[690],[574,3383,3385],{"className":3384},[695,696,697,698],[574,3386,3388],{"className":3387},[659,698],[574,3389,1341],{"className":3390},[659,698],[574,3392,596],{"className":3393},[648],[574,3395,854],{"className":3396},[659],[574,3398,622],{"className":3399},[750],[574,3401],{"className":3402,"style":1230},[758],[574,3404,1167],{"className":3405},[1234],[574,3407],{"className":3408,"style":1230},[758],[574,3410,3412,3415,3477,3480,3483],{"className":3411},[635],[574,3413],{"className":3414,"style":2851},[639],[574,3416,3418,3421,3474],{"className":3417},[659],[574,3419],{"className":3420},[648,666],[574,3422,3424],{"className":3423},[601],[574,3425,3427,3466],{"className":3426},[673,674],[574,3428,3430,3463],{"className":3429},[678],[574,3431,3433,3444,3452],{"className":3432,"style":2127},[682],[574,3434,3435,3438],{"style":2255},[574,3436],{"className":3437,"style":691},[690],[574,3439,3441],{"className":3440},[659],[574,3442,610],{"className":3443},[659],[574,3445,3446,3449],{"style":707},[574,3447],{"className":3448,"style":691},[690],[574,3450],{"className":3451,"style":715},[714],[574,3453,3454,3457],{"style":2194},[574,3455],{"className":3456,"style":691},[690],[574,3458,3460],{"className":3459},[659],[574,3461,610],{"className":3462},[659],[574,3464,737],{"className":3465},[736],[574,3467,3469],{"className":3468},[678],[574,3470,3472],{"className":3471,"style":2909},[682],[574,3473],{},[574,3475],{"className":3476},[750,666],[574,3478],{"className":3479,"style":1230},[758],[574,3481,1167],{"className":3482},[1234],[574,3484],{"className":3485,"style":1230},[758],[574,3487,3489,3492],{"className":3488},[635],[574,3490],{"className":3491,"style":1017},[639],[574,3493,854],{"className":3494},[659],[560,3496,3498],{"id":3497},"typische-fehler","Typische Fehler",[3500,3501,3502,3702,4023],"ul",{},[3503,3504,3505,3543,3544,3701],"li",{},[574,3506,3508,3525],{"className":3507},[577],[574,3509,3511],{"className":3510},[581],[583,3512,3513],{"xmlns":585},[587,3514,3515,3523],{},[590,3516,3517,3519,3521],{},[604,3518,1149],{},[593,3520,1152],{},[604,3522,867],{},[624,3524,1567],{"encoding":626},[574,3526,3528],{"className":3527,"ariaHidden":595},[631],[574,3529,3531,3534,3537,3540],{"className":3530},[635],[574,3532],{"className":3533,"style":1213},[639],[574,3535,1149],{"className":3536},[1190],[574,3538],{"className":3539,"style":759},[758],[574,3541,867],{"className":3542},[659,731]," mit ",[574,3545,3547,3580],{"className":3546},[577],[574,3548,3550],{"className":3549},[581],[583,3551,3552],{"xmlns":585},[587,3553,3554,3577],{},[590,3555,3556,3568,3570,3573,3575],{},[601,3557,3558,3560],{},[608,3559,854],{},[590,3561,3562,3564,3566],{},[604,3563,1812],{},[593,3565,1152],{},[604,3567,867],{},[593,3569,1167],{},[604,3571,3572],{},"cot",[593,3574,1152],{},[604,3576,867],{},[624,3578,3579],{"encoding":626},"\\frac{1}{\\tan x} = \\cot x",[574,3581,3583,3686],{"className":3582,"ariaHidden":595},[631],[574,3584,3586,3590,3677,3680,3683],{"className":3585},[635],[574,3587],{"className":3588,"style":3589},[639],"height:1.1901em;vertical-align:-0.345em;",[574,3591,3593,3596,3674],{"className":3592},[659],[574,3594],{"className":3595},[648,666],[574,3597,3599],{"className":3598},[601],[574,3600,3602,3666],{"className":3601},[673,674],[574,3603,3605,3663],{"className":3604},[678],[574,3606,3608,3641,3649],{"className":3607,"style":901},[682],[574,3609,3610,3613],{"style":686},[574,3611],{"className":3612,"style":691},[690],[574,3614,3616],{"className":3615},[695,696,697,698],[574,3617,3619,3634,3638],{"className":3618},[659,698],[574,3620,3622,3626,3630],{"className":3621},[1190,698],[574,3623,3625],{"className":3624},[698],"t",[574,3627,3629],{"className":3628},[698],"a",[574,3631,3633],{"className":3632},[698],"n",[574,3635],{"className":3636,"style":3637},[758,698],"margin-right:0.1952em;",[574,3639,867],{"className":3640},[659,731,698],[574,3642,3643,3646],{"style":707},[574,3644],{"className":3645,"style":691},[690],[574,3647],{"className":3648,"style":715},[714],[574,3650,3651,3654],{"style":718},[574,3652],{"className":3653,"style":691},[690],[574,3655,3657],{"className":3656},[695,696,697,698],[574,3658,3660],{"className":3659},[659,698],[574,3661,854],{"className":3662},[659,698],[574,3664,737],{"className":3665},[736],[574,3667,3669],{"className":3668},[678],[574,3670,3672],{"className":3671,"style":744},[682],[574,3673],{},[574,3675],{"className":3676},[750,666],[574,3678],{"className":3679,"style":1230},[758],[574,3681,1167],{"className":3682},[1234],[574,3684],{"className":3685,"style":1230},[758],[574,3687,3689,3692,3695,3698],{"className":3688},[635],[574,3690],{"className":3691,"style":1213},[639],[574,3693,3572],{"className":3694},[1190],[574,3696],{"className":3697,"style":759},[758],[574,3699,867],{"className":3700},[659,731]," verwechseln. Der Arkustangens ist die Umkehrfunktion, nicht der Kehrwert.",[3503,3703,3704,3705,3733,3734,3987,3988,4022],{},"Bei verketteten Funktionen nur ",[574,3706,3708,3721],{"className":3707},[577],[574,3709,3711],{"className":3710},[581],[583,3712,3713],{"xmlns":585},[587,3714,3715,3719],{},[590,3716,3717],{},[604,3718,867],{},[624,3720,867],{"encoding":626},[574,3722,3724],{"className":3723,"ariaHidden":595},[631],[574,3725,3727,3730],{"className":3726},[635],[574,3728],{"className":3729,"style":1858},[639],[574,3731,867],{"className":3732},[659,731]," durch die innere Funktion ersetzen: ",[574,3735,3737,3789],{"className":3736},[577],[574,3738,3740],{"className":3739},[581],[583,3741,3742],{"xmlns":585},[587,3743,3744,3786],{},[590,3745,3746,3748,3750,3752,3754,3760,3762,3768,3770],{},[593,3747,596],{"stretchy":1327},[604,3749,1149],{},[593,3751,1152],{},[593,3753,596],{"stretchy":1327},[863,3755,3756,3758],{},[604,3757,867],{},[608,3759,610],{},[593,3761,622],{"stretchy":1327},[863,3763,3764,3766],{},[593,3765,622],{"stretchy":1327},[593,3767,1341],{"mathvariant":1159,"lspace":1340,"rspace":1340},[593,3769,1167],{},[601,3771,3772,3774],{},[608,3773,854],{},[590,3775,3776,3778,3780],{},[608,3777,854],{},[593,3779,861],{},[863,3781,3782,3784],{},[604,3783,867],{},[608,3785,3061],{},[624,3787,3788],{"encoding":626},"(\\arctan(x^2))' = \\frac{1}{1 + x^4}",[574,3790,3792,3881],{"className":3791,"ariaHidden":595},[631],[574,3793,3795,3799,3802,3805,3808,3837,3840,3872,3875,3878],{"className":3794},[635],[574,3796],{"className":3797,"style":3798},[639],"height:1.0641em;vertical-align:-0.25em;",[574,3800,596],{"className":3801},[648],[574,3803,1149],{"className":3804},[1190],[574,3806,596],{"className":3807},[648],[574,3809,3811,3814],{"className":3810},[659],[574,3812,867],{"className":3813},[659,731],[574,3815,3817],{"className":3816},[929],[574,3818,3820],{"className":3819},[673],[574,3821,3823],{"className":3822},[678],[574,3824,3826],{"className":3825,"style":2948},[682],[574,3827,3828,3831],{"style":1411},[574,3829],{"className":3830,"style":1415},[690],[574,3832,3834],{"className":3833},[695,696,697,698],[574,3835,610],{"className":3836},[659,698],[574,3838,622],{"className":3839},[750],[574,3841,3843,3846],{"className":3842},[750],[574,3844,622],{"className":3845},[750],[574,3847,3849],{"className":3848},[929],[574,3850,3852],{"className":3851},[673],[574,3853,3855],{"className":3854},[678],[574,3856,3858],{"className":3857,"style":1408},[682],[574,3859,3860,3863],{"style":1411},[574,3861],{"className":3862,"style":1415},[690],[574,3864,3866],{"className":3865},[695,696,697,698],[574,3867,3869],{"className":3868},[659,698],[574,3870,1341],{"className":3871},[659,698],[574,3873],{"className":3874,"style":1230},[758],[574,3876,1167],{"className":3877},[1234],[574,3879],{"className":3880,"style":1230},[758],[574,3882,3884,3887],{"className":3883},[635],[574,3885],{"className":3886,"style":882},[639],[574,3888,3890,3893,3984],{"className":3889},[659],[574,3891],{"className":3892},[648,666],[574,3894,3896],{"className":3895},[601],[574,3897,3899,3976],{"className":3898},[673,674],[574,3900,3902,3973],{"className":3901},[678],[574,3903,3905,3951,3959],{"className":3904,"style":901},[682],[574,3906,3907,3910],{"style":686},[574,3908],{"className":3909,"style":691},[690],[574,3911,3913],{"className":3912},[695,696,697,698],[574,3914,3916,3919,3922],{"className":3915},[659,698],[574,3917,854],{"className":3918},[659,698],[574,3920,861],{"className":3921},[919,698],[574,3923,3925,3928],{"className":3924},[659,698],[574,3926,867],{"className":3927},[659,731,698],[574,3929,3931],{"className":3930},[929],[574,3932,3934],{"className":3933},[673],[574,3935,3937],{"className":3936},[678],[574,3938,3940],{"className":3939,"style":939},[682],[574,3941,3942,3945],{"style":942},[574,3943],{"className":3944,"style":946},[690],[574,3946,3948],{"className":3947},[695,950,655,698],[574,3949,3061],{"className":3950},[659,698],[574,3952,3953,3956],{"style":707},[574,3954],{"className":3955,"style":691},[690],[574,3957],{"className":3958,"style":715},[714],[574,3960,3961,3964],{"style":718},[574,3962],{"className":3963,"style":691},[690],[574,3965,3967],{"className":3966},[695,696,697,698],[574,3968,3970],{"className":3969},[659,698],[574,3971,854],{"className":3972},[659,698],[574,3974,737],{"className":3975},[736],[574,3977,3979],{"className":3978},[678],[574,3980,3982],{"className":3981,"style":985},[682],[574,3983],{},[574,3985],{"className":3986},[750,666]," ist falsch, die innere Ableitung ",[574,3989,3991,4007],{"className":3990},[577],[574,3992,3994],{"className":3993},[581],[583,3995,3996],{"xmlns":585},[587,3997,3998,4004],{},[590,3999,4000,4002],{},[608,4001,610],{},[604,4003,867],{},[624,4005,4006],{"encoding":626},"2x",[574,4008,4010],{"className":4009,"ariaHidden":595},[631],[574,4011,4013,4016,4019],{"className":4012},[635],[574,4014],{"className":4015,"style":1017},[639],[574,4017,610],{"className":4018},[659],[574,4020,867],{"className":4021},[659,731]," 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x^2}}",[574,4199,4201],{"className":4200,"ariaHidden":595},[631],[574,4202,4204,4208],{"className":4203},[635],[574,4205],{"className":4206,"style":4207},[639],"height:1.3831em;vertical-align:-0.538em;",[574,4209,4211,4214,4368],{"className":4210},[659],[574,4212],{"className":4213},[648,666],[574,4215,4217],{"className":4216},[601],[574,4218,4220,4359],{"className":4219},[673,674],[574,4221,4223,4356],{"className":4222},[678],[574,4224,4226,4334,4342],{"className":4225,"style":901},[682],[574,4227,4229,4232],{"style":4228},"top:-2.5445em;",[574,4230],{"className":4231,"style":691},[690],[574,4233,4235],{"className":4234},[695,696,697,698],[574,4236,4238],{"className":4237},[659,698],[574,4239,4242],{"className":4240},[659,4241,698],"sqrt",[574,4243,4245,4325],{"className":4244},[673,674],[574,4246,4248,4322],{"className":4247},[678],[574,4249,4252,4299],{"className":4250,"style":4251},[682],"height:0.9221em;",[574,4253,4257,4260],{"className":4254,"style":4256},[4255],"svg-align","top:-3em;",[574,4258],{"className":4259,"style":691},[690],[574,4261,4264,4267,4270],{"className":4262,"style":4263},[659,698],"padding-left:0.833em;",[574,4265,854],{"className":4266},[659,698],[574,4268,599],{"className":4269},[919,698],[574,4271,4273,4276],{"className":4272},[659,698],[574,4274,867],{"className":4275},[659,731,698],[574,4277,4279],{"className":4278},[929],[574,4280,4282],{"className":4281},[673],[574,4283,4285],{"className":4284},[678],[574,4286,4288],{"className":4287,"style":939},[682],[574,4289,4290,4293],{"style":942},[574,4291],{"className":4292,"style":946},[690],[574,4294,4296],{"className":4295},[695,950,655,698],[574,4297,610],{"className":4298},[659,698],[574,4300,4302,4305],{"style":4301},"top:-2.8821em;",[574,4303],{"className":4304,"style":691},[690],[574,4306,4310],{"className":4307,"style":4309},[4308,698],"hide-tail","min-width:0.853em;height:1.08em;",[4311,4312,4318],"svg",{"xmlns":4313,"width":4314,"height":4315,"viewBox":4316,"preserveAspectRatio":4317},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[4319,4320],"path",{"d":4321},"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 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Das ist die Ableitung des Arkussinus.",{"title":4373,"searchDepth":4374,"depth":4374,"links":4375},"",2,[4376,4377,4378,4379],{"id":562,"depth":4374,"text":563},{"id":1729,"depth":4374,"text":1730},{"id":2341,"depth":4374,"text":2342},{"id":3497,"depth":4374,"text":3498},[4381,4384,4386,4389,4391,4393,4396,4398],{"lhs":4382,"rhs":4383},"1\u002F(1 + tan(atan(x))^2)","1\u002F(1 + x^2)",{"lhs":4385,"rhs":2364},"round((atan(x+1e-5) - atan(x-1e-5))\u002F(2e-5) - 1\u002F(1 + x^2), 6)",{"lhs":4385,"rhs":2364,"where":4387},{"x":4388},-2,{"lhs":4390,"rhs":2364},"round(((pi\u002F2 - atan(x+1e-5)) - (pi\u002F2 - atan(x-1e-5)))\u002F(2e-5) + 1\u002F(1 + x^2), 6)",{"lhs":4392,"rhs":854},"1\u002F(1 + 0^2)",{"lhs":4394,"rhs":4395},"1\u002F(1 + 1^2)","0.5",{"lhs":4397,"rhs":2364},"round((atan((x+1e-5)^2) - atan((x-1e-5)^2))\u002F(2e-5) - 2*x\u002F(1 + x^4), 6)",{"lhs":4399,"rhs":854},"2*1\u002F(1 + 1^4)",null,"md","derivative-arctan","f(x) = \\arctan x \\;\\Rightarrow\\; f'(x) = \\frac{1}{1 + x^2}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>arctan\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 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