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\\frac{\\pi}{2}\\right)",[568,1101,1103,1127],{"className":1102,"ariaHidden":606},[605],[568,1104,1106,1109,1112,1115,1118,1121,1124],{"className":1105},[610],[568,1107],{"className":1108,"style":894},[614],[568,1110,804],{"className":1111},[759],[568,1113],{"className":1114,"style":755},[754],[568,1116,734],{"className":1117},[619,689],[568,1119],{"className":1120,"style":874},[754],[568,1122,1070],{"className":1123},[881],[568,1125],{"className":1126,"style":874},[754],[568,1128,1130,1134,1137,1141,1144],{"className":1129},[610],[568,1131],{"className":1132,"style":1133},[614],"height:1.2em;vertical-align:-0.35em;",[568,1135,728],{"className":1136},[759],[568,1138],{"className":1139,"style":1140},[754],"margin-right:-0.1667em;",[568,1142],{"className":1143,"style":755},[754],[568,1145,1148,1158,1161,1165,1169,1172,1240],{"className":1146},[1147],"minner",[568,1149,1153],{"className":1150,"style":1152},[623,1151],"delimcenter","top:0em;",[568,1154,1082],{"className":1155},[1156,1157],"delimsizing","size1",[568,1159,734],{"className":1160},[619,689],[568,1162],{"className":1163,"style":1164},[754],"margin-right:0.2222em;",[568,1166,1087],{"className":1167},[1168],"mbin",[568,1170],{"className":1171,"style":1164},[754],[568,1173,1175,1178,1237],{"className":1174},[619],[568,1176],{"className":1177},[623,624],[568,1179,1181],{"className":1180},[587],[568,1182,1184,1229],{"className":1183},[631,632],[568,1185,1187,1226],{"className":1186},[636],[568,1188,1190,1204,1212],{"className":1189,"style":641},[640],[568,1191,1192,1195],{"style":644},[568,1193],{"className":1194,"style":649},[648],[568,1196,1198],{"className":1197},[653,654,655,656],[568,1199,1201],{"className":1200},[619,656],[568,1202,596],{"className":1203},[619,656],[568,1205,1206,1209],{"style":665},[568,1207],{"className":1208,"style":649},[648],[568,1210],{"className":1211,"style":673},[672],[568,1213,1214,1217],{"style":676},[568,1215],{"className":1216,"style":649},[648],[568,1218,1220],{"className":1219},[653,654,655,656],[568,1221,1223],{"className":1222},[619,656],[568,1224,592],{"className":1225,"style":690},[619,689,656],[568,1227,695],{"className":1228},[694],[568,1230,1232],{"className":1231},[636],[568,1233,1235],{"className":1234,"style":702},[640],[568,1236],{},[568,1238],{"className":1239},[708,624],[568,1241,1243],{"className":1242,"style":1152},[708,1151],[568,1244,1096],{"className":1245},[1156,1157]," und der Kettenregel (innere Ableitung ",[568,1248,1250,1264],{"className":1249},[571],[568,1251,1253],{"className":1252},[575],[577,1254,1255],{"xmlns":579},[581,1256,1257,1262],{},[584,1258,1259],{},[594,1260,1261],{},"1",[598,1263,1261],{"encoding":600},[568,1265,1267],{"className":1266,"ariaHidden":606},[605],[568,1268,1270,1274],{"className":1269},[610],[568,1271],{"className":1272,"style":1273},[614],"height:0.6444em;",[568,1275,1261],{"className":1276},[619],"):",[568,1279,1281],{"className":1280},[773],[568,1282,1284,1349],{"className":1283},[571],[568,1285,1287],{"className":1286},[575],[577,1288,1289],{"xmlns":579,"display":782},[581,1290,1291,1346],{},[584,1292,1293,1296,1298,1300,1302,1312,1314,1316,1318,1320,1336,1338,1340,1342,1344],{},[723,1294,1082],{"stretchy":1295},"false",[590,1297,804],{},[723,1299,731],{},[590,1301,734],{},[1303,1304,1305,1307],"msup",{},[723,1306,1096],{"stretchy":1295},[723,1308,1311],{"mathvariant":1309,"lspace":1310,"rspace":1310},"normal","0em","′",[723,1313,1070],{},[590,1315,804],{},[723,1317,731],{},[794,1319,1077],{},[584,1321,1322,1324,1326,1328,1334],{},[723,1323,1082],{"fence":606},[590,1325,734],{},[723,1327,1087],{},[587,1329,1330,1332],{},[590,1331,592],{},[594,1333,596],{},[723,1335,1096],{"fence":606},[723,1337,1070],{},[723,1339,725],{},[590,1341,728],{},[723,1343,731],{},[590,1345,734],{},[598,1347,1348],{"encoding":600},"(\\cos x)' = \\cos\\!\\left(x + \\frac{\\pi}{2}\\right) = -\\sin x",[568,1350,1352,1416,1535],{"className":1351,"ariaHidden":606},[605],[568,1353,1355,1359,1362,1365,1368,1371,1407,1410,1413],{"className":1354},[610],[568,1356],{"className":1357,"style":1358},[614],"height:1.0519em;vertical-align:-0.25em;",[568,1360,1082],{"className":1361},[623],[568,1363,804],{"className":1364},[759],[568,1366],{"className":1367,"style":755},[754],[568,1369,734],{"className":1370},[619,689],[568,1372,1374,1377],{"className":1373},[708],[568,1375,1096],{"className":1376},[708],[568,1378,1381],{"className":1379},[1380],"msupsub",[568,1382,1384],{"className":1383},[631],[568,1385,1387],{"className":1386},[636],[568,1388,1391],{"className":1389,"style":1390},[640],"height:0.8019em;",[568,1392,1394,1398],{"style":1393},"top:-3.113em;margin-right:0.05em;",[568,1395],{"className":1396,"style":1397},[648],"height:2.7em;",[568,1399,1401],{"className":1400},[653,654,655,656],[568,1402,1404],{"className":1403},[619,656],[568,1405,1311],{"className":1406},[619,656],[568,1408],{"className":1409,"style":874},[754],[568,1411,1070],{"className":1412},[881],[568,1414],{"className":1415,"style":874},[754],[568,1417,1419,1423,1426,1429,1432,1526,1529,1532],{"className":1418},[610],[568,1420],{"className":1421,"style":1422},[614],"height:1.836em;vertical-align:-0.686em;",[568,1424,804],{"className":1425},[759],[568,1427],{"className":1428,"style":1140},[754],[568,1430],{"className":1431,"style":755},[754],[568,1433,1435,1442,1445,1448,1451,1454,1520],{"className":1434},[1147],[568,1436,1438],{"className":1437,"style":1152},[623,1151],[568,1439,1082],{"className":1440},[1156,1441],"size2",[568,1443,734],{"className":1444},[619,689],[568,1446],{"className":1447,"style":1164},[754],[568,1449,1087],{"className":1450},[1168],[568,1452],{"className":1453,"style":1164},[754],[568,1455,1457,1460,1517],{"className":1456},[619],[568,1458],{"className":1459},[623,624],[568,1461,1463],{"className":1462},[587],[568,1464,1466,1508],{"className":1465},[631,632],[568,1467,1469,1505],{"className":1468},[636],[568,1470,1473,1485,1493],{"className":1471,"style":1472},[640],"height:1.1076em;",[568,1474,1476,1479],{"style":1475},"top:-2.314em;",[568,1477],{"className":1478,"style":649},[648],[568,1480,1482],{"className":1481},[619],[568,1483,596],{"className":1484},[619],[568,1486,1487,1490],{"style":665},[568,1488],{"className":1489,"style":649},[648],[568,1491],{"className":1492,"style":673},[672],[568,1494,1496,1499],{"style":1495},"top:-3.677em;",[568,1497],{"className":1498,"style":649},[648],[568,1500,1502],{"className":1501},[619],[568,1503,592],{"className":1504,"style":690},[619,689],[568,1506,695],{"className":1507},[694],[568,1509,1511],{"className":1510},[636],[568,1512,1515],{"className":1513,"style":1514},[640],"height:0.686em;",[568,1516],{},[568,1518],{"className":1519},[708,624],[568,1521,1523],{"className":1522,"style":1152},[708,1151],[568,1524,1096],{"className":1525},[1156,1441],[568,1527],{"className":1528,"style":874},[754],[568,1530,1070],{"className":1531},[881],[568,1533],{"className":1534,"style":874},[754],[568,1536,1538,1541,1544,1547,1550,1553],{"className":1537},[610],[568,1539],{"className":1540,"style":747},[614],[568,1542,725],{"className":1543},[619],[568,1545],{"className":1546,"style":755},[754],[568,1548,728],{"className":1549},[759],[568,1551],{"className":1552,"style":755},[754],[568,1554,734],{"className":1555},[619,689],[559,1557,1559],{"id":1558},"beispiele","Beispiele",[568,1561,1563],{"className":1562},[773],[568,1564,1566,1661],{"className":1565},[571],[568,1567,1569],{"className":1568},[575],[577,1570,1571],{"xmlns":579,"display":782},[581,1572,1573,1658],{},[584,1574,1575,1578,1580,1582,1584,1586,1589,1591,1593,1595,1597,1600,1602,1608,1610,1612,1614,1616,1618,1620,1622,1624,1626,1629,1632,1638,1640,1652,1654,1656],{},[590,1576,1577],{},"f",[723,1579,1082],{"stretchy":1295},[590,1581,734],{},[723,1583,1096],{"stretchy":1295},[723,1585,1070],{},[594,1587,1588],{},"4",[590,1590,804],{},[723,1592,731],{},[590,1594,734],{},[794,1596,796],{},[723,1598,1599],{},"⇒",[794,1601,796],{},[1303,1603,1604,1606],{},[590,1605,1577],{},[723,1607,1311],{"mathvariant":1309,"lspace":1310,"rspace":1310},[723,1609,1082],{"stretchy":1295},[590,1611,734],{},[723,1613,1096],{"stretchy":1295},[723,1615,1070],{},[723,1617,725],{},[594,1619,1588],{},[590,1621,728],{},[723,1623,731],{},[590,1625,734],{},[723,1627,1628],{"separator":606},",",[754,1630],{"width":1631},"1em",[1303,1633,1634,1636],{},[590,1635,1577],{},[723,1637,1311],{"mathvariant":1309,"lspace":1310,"rspace":1310},[794,1639,1077],{},[584,1641,1642,1644,1650],{},[723,1643,1082],{"fence":606},[587,1645,1646,1648],{},[590,1647,592],{},[594,1649,596],{},[723,1651,1096],{"fence":606},[723,1653,1070],{},[723,1655,725],{},[594,1657,1588],{},[598,1659,1660],{"encoding":600},"f(x) = 4\\cos x \\;\\Rightarrow\\; f'(x) = -4\\sin x, \\quad f'\\!\\left(\\frac{\\pi}{2}\\right) = -4",[568,1662,1664,1693,1729,1785,1944],{"className":1663,"ariaHidden":606},[605],[568,1665,1667,1671,1675,1678,1681,1684,1687,1690],{"className":1666},[610],[568,1668],{"className":1669,"style":1670},[614],"height:1em;vertical-align:-0.25em;",[568,1672,1577],{"className":1673,"style":1674},[619,689],"margin-right:0.1076em;",[568,1676,1082],{"className":1677},[623],[568,1679,734],{"className":1680},[619,689],[568,1682,1096],{"className":1683},[708],[568,1685],{"className":1686,"style":874},[754],[568,1688,1070],{"className":1689},[881],[568,1691],{"className":1692,"style":874},[754],[568,1694,1696,1699,1702,1705,1708,1711,1714,1717,1720,1723,1726],{"className":1695},[610],[568,1697],{"className":1698,"style":1273},[614],[568,1700,1588],{"className":1701},[619],[568,1703],{"className":1704,"style":755},[754],[568,1706,804],{"className":1707},[759],[568,1709],{"className":1710,"style":755},[754],[568,1712,734],{"className":1713},[619,689],[568,1715],{"className":1716,"style":874},[754],[568,1718],{"className":1719,"style":874},[754],[568,1721,1599],{"className":1722},[881],[568,1724],{"className":1725,"style":874},[754],[568,1727],{"className":1728,"style":874},[754],[568,1730,1732,1735,1767,1770,1773,1776,1779,1782],{"className":1731},[610],[568,1733],{"className":1734,"style":1358},[614],[568,1736,1738,1741],{"className":1737},[619],[568,1739,1577],{"className":1740,"style":1674},[619,689],[568,1742,1744],{"className":1743},[1380],[568,1745,1747],{"className":1746},[631],[568,1748,1750],{"className":1749},[636],[568,1751,1753],{"className":1752,"style":1390},[640],[568,1754,1755,1758],{"style":1393},[568,1756],{"className":1757,"style":1397},[648],[568,1759,1761],{"className":1760},[653,654,655,656],[568,1762,1764],{"className":1763},[619,656],[568,1765,1311],{"className":1766},[619,656],[568,1768,1082],{"className":1769},[623],[568,1771,734],{"className":1772},[619,689],[568,1774,1096],{"className":1775},[708],[568,1777],{"className":1778,"style":874},[754],[568,1780,1070],{"className":1781},[881],[568,1783],{"className":1784,"style":874},[754],[568,1786,1788,1791,1794,1797,1800,1803,1806,1809,1813,1817,1820,1852,1855,1858,1935,1938,1941],{"className":1787},[610],[568,1789],{"className":1790,"style":1422},[614],[568,1792,725],{"className":1793},[619],[568,1795,1588],{"className":1796},[619],[568,1798],{"className":1799,"style":755},[754],[568,1801,728],{"className":1802},[759],[568,1804],{"className":1805,"style":755},[754],[568,1807,734],{"className":1808},[619,689],[568,1810,1628],{"className":1811},[1812],"mpunct",[568,1814],{"className":1815,"style":1816},[754],"margin-right:1em;",[568,1818],{"className":1819,"style":755},[754],[568,1821,1823,1826],{"className":1822},[619],[568,1824,1577],{"className":1825,"style":1674},[619,689],[568,1827,1829],{"className":1828},[1380],[568,1830,1832],{"className":1831},[631],[568,1833,1835],{"className":1834},[636],[568,1836,1838],{"className":1837,"style":1390},[640],[568,1839,1840,1843],{"style":1393},[568,1841],{"className":1842,"style":1397},[648],[568,1844,1846],{"className":1845},[653,654,655,656],[568,1847,1849],{"className":1848},[619,656],[568,1850,1311],{"className":1851},[619,656],[568,1853],{"className":1854,"style":1140},[754],[568,1856],{"className":1857,"style":755},[754],[568,1859,1861,1867,1929],{"className":1860},[1147],[568,1862,1864],{"className":1863,"style":1152},[623,1151],[568,1865,1082],{"className":1866},[1156,1441],[568,1868,1870,1873,1926],{"className":1869},[619],[568,1871],{"className":1872},[623,624],[568,1874,1876],{"className":1875},[587],[568,1877,1879,1918],{"className":1878},[631,632],[568,1880,1882,1915],{"className":1881},[636],[568,1883,1885,1896,1904],{"className":1884,"style":1472},[640],[568,1886,1887,1890],{"style":1475},[568,1888],{"className":1889,"style":649},[648],[568,1891,1893],{"className":1892},[619],[568,1894,596],{"className":1895},[619],[568,1897,1898,1901],{"style":665},[568,1899],{"className":1900,"style":649},[648],[568,1902],{"className":1903,"style":673},[672],[568,1905,1906,1909],{"style":1495},[568,1907],{"className":1908,"style":649},[648],[568,1910,1912],{"className":1911},[619],[568,1913,592],{"className":1914,"style":690},[619,689],[568,1916,695],{"className":1917},[694],[568,1919,1921],{"className":1920},[636],[568,1922,1924],{"className":1923,"style":1514},[640],[568,1925],{},[568,1927],{"className":1928},[708,624],[568,1930,1932],{"className":1931,"style":1152},[708,1151],[568,1933,1096],{"className":1934},[1156,1441],[568,1936],{"className":1937,"style":874},[754],[568,1939,1070],{"className":1940},[881],[568,1942],{"className":1943,"style":874},[754],[568,1945,1947,1951,1954],{"className":1946},[610],[568,1948],{"className":1949,"style":1950},[614],"height:0.7278em;vertical-align:-0.0833em;",[568,1952,725],{"className":1953},[619],[568,1955,1588],{"className":1956},[619],[564,1958,1959],{},"Mit der Kettenregel:",[568,1961,1963],{"className":1962},[773],[568,1964,1966,2067],{"className":1965},[571],[568,1967,1969],{"className":1968},[575],[577,1970,1971],{"xmlns":579,"display":782},[581,1972,1973,2064],{},[584,1974,1975,1977,1979,1981,1983,1985,1987,1989,1991,1997,1999,2001,2003,2005,2011,2013,2015,2017,2019,2021,2023,2025,2027,2033,2035,2038,2040,2042,2044,2046,2048,2050,2052,2054,2056,2062],{},[590,1976,1577],{},[723,1978,1082],{"stretchy":1295},[590,1980,734],{},[723,1982,1096],{"stretchy":1295},[723,1984,1070],{},[590,1986,804],{},[723,1988,731],{},[723,1990,1082],{"stretchy":1295},[1303,1992,1993,1995],{},[590,1994,734],{},[594,1996,596],{},[723,1998,1096],{"stretchy":1295},[794,2000,796],{},[723,2002,1599],{},[794,2004,796],{},[1303,2006,2007,2009],{},[590,2008,1577],{},[723,2010,1311],{"mathvariant":1309,"lspace":1310,"rspace":1310},[723,2012,1082],{"stretchy":1295},[590,2014,734],{},[723,2016,1096],{"stretchy":1295},[723,2018,1070],{},[723,2020,725],{},[590,2022,728],{},[723,2024,731],{},[723,2026,1082],{"stretchy":1295},[1303,2028,2029,2031],{},[590,2030,734],{},[594,2032,596],{},[723,2034,1096],{"stretchy":1295},[723,2036,2037],{},"⋅",[594,2039,596],{},[590,2041,734],{},[723,2043,1070],{},[723,2045,725],{},[594,2047,596],{},[590,2049,734],{},[590,2051,728],{},[723,2053,731],{},[723,2055,1082],{"stretchy":1295},[1303,2057,2058,2060],{},[590,2059,734],{},[594,2061,596],{},[723,2063,1096],{"stretchy":1295},[598,2065,2066],{"encoding":600},"f(x) = \\cos(x^2) \\;\\Rightarrow\\; f'(x) = -\\sin(x^2) \\cdot 2x = -2x\\sin(x^2)",[568,2068,2070,2097,2158,2214,2273,2294],{"className":2069,"ariaHidden":606},[605],[568,2071,2073,2076,2079,2082,2085,2088,2091,2094],{"className":2072},[610],[568,2074],{"className":2075,"style":1670},[614],[568,2077,1577],{"className":2078,"style":1674},[619,689],[568,2080,1082],{"className":2081},[623],[568,2083,734],{"className":2084},[619,689],[568,2086,1096],{"className":2087},[708],[568,2089],{"className":2090,"style":874},[754],[568,2092,1070],{"className":2093},[881],[568,2095],{"className":2096,"style":874},[754],[568,2098,2100,2104,2107,2110,2140,2143,2146,2149,2152,2155],{"className":2099},[610],[568,2101],{"className":2102,"style":2103},[614],"height:1.1141em;vertical-align:-0.25em;",[568,2105,804],{"className":2106},[759],[568,2108,1082],{"className":2109},[623],[568,2111,2113,2116],{"className":2112},[619],[568,2114,734],{"className":2115},[619,689],[568,2117,2119],{"className":2118},[1380],[568,2120,2122],{"className":2121},[631],[568,2123,2125],{"className":2124},[636],[568,2126,2129],{"className":2127,"style":2128},[640],"height:0.8641em;",[568,2130,2131,2134],{"style":1393},[568,2132],{"className":2133,"style":1397},[648],[568,2135,2137],{"className":2136},[653,654,655,656],[568,2138,596],{"className":2139},[619,656],[568,2141,1096],{"className":2142},[708],[568,2144],{"className":2145,"style":874},[754],[568,2147],{"className":2148,"style":874},[754],[568,2150,1599],{"className":2151},[881],[568,2153],{"className":2154,"style":874},[754],[568,2156],{"className":2157,"style":874},[754],[568,2159,2161,2164,2196,2199,2202,2205,2208,2211],{"className":2160},[610],[568,2162],{"className":2163,"style":1358},[614],[568,2165,2167,2170],{"className":2166},[619],[568,2168,1577],{"className":2169,"style":1674},[619,689],[568,2171,2173],{"className":2172},[1380],[568,2174,2176],{"className":2175},[631],[568,2177,2179],{"className":2178},[636],[568,2180,2182],{"className":2181,"style":1390},[640],[568,2183,2184,2187],{"style":1393},[568,2185],{"className":2186,"style":1397},[648],[568,2188,2190],{"className":2189},[653,654,655,656],[568,2191,2193],{"className":2192},[619,656],[568,2194,1311],{"className":2195},[619,656],[568,2197,1082],{"className":2198},[623],[568,2200,734],{"className":2201},[619,689],[568,2203,1096],{"className":2204},[708],[568,2206],{"className":2207,"style":874},[754],[568,2209,1070],{"className":2210},[881],[568,2212],{"className":2213,"style":874},[754],[568,2215,2217,2220,2223,2226,2229,2232,2261,2264,2267,2270],{"className":2216},[610],[568,2218],{"className":2219,"style":2103},[614],[568,2221,725],{"className":2222},[619],[568,2224],{"className":2225,"style":755},[754],[568,2227,728],{"className":2228},[759],[568,2230,1082],{"className":2231},[623],[568,2233,2235,2238],{"className":2234},[619],[568,2236,734],{"className":2237},[619,689],[568,2239,2241],{"className":2240},[1380],[568,2242,2244],{"className":2243},[631],[568,2245,2247],{"className":2246},[636],[568,2248,2250],{"className":2249,"style":2128},[640],[568,2251,2252,2255],{"style":1393},[568,2253],{"className":2254,"style":1397},[648],[568,2256,2258],{"className":2257},[653,654,655,656],[568,2259,596],{"className":2260},[619,656],[568,2262,1096],{"className":2263},[708],[568,2265],{"className":2266,"style":1164},[754],[568,2268,2037],{"className":2269},[1168],[568,2271],{"className":2272,"style":1164},[754],[568,2274,2276,2279,2282,2285,2288,2291],{"className":2275},[610],[568,2277],{"className":2278,"style":1273},[614],[568,2280,596],{"className":2281},[619],[568,2283,734],{"className":2284},[619,689],[568,2286],{"className":2287,"style":874},[754],[568,2289,1070],{"className":2290},[881],[568,2292],{"className":2293,"style":874},[754],[568,2295,2297,2300,2303,2306,2309,2312,2315,2318,2347],{"className":2296},[610],[568,2298],{"className":2299,"style":2103},[614],[568,2301,725],{"className":2302},[619],[568,2304,596],{"className":2305},[619],[568,2307,734],{"className":2308},[619,689],[568,2310],{"className":2311,"style":755},[754],[568,2313,728],{"className":2314},[759],[568,2316,1082],{"className":2317},[623],[568,2319,2321,2324],{"className":2320},[619],[568,2322,734],{"className":2323},[619,689],[568,2325,2327],{"className":2326},[1380],[568,2328,2330],{"className":2329},[631],[568,2331,2333],{"className":2332},[636],[568,2334,2336],{"className":2335,"style":2128},[640],[568,2337,2338,2341],{"style":1393},[568,2339],{"className":2340,"style":1397},[648],[568,2342,2344],{"className":2343},[653,654,655,656],[568,2345,596],{"className":2346},[619,656],[568,2348,1096],{"className":2349},[708],[559,2351,2353],{"id":2352},"typische-fehler","Typische Fehler",[2355,2356,2357,2479,2652],"ul",{},[2358,2359,2360,2361,2478],"li",{},"Das Minuszeichen vergessen: ",[568,2362,2364,2398],{"className":2363},[571],[568,2365,2367],{"className":2366},[575],[577,2368,2369],{"xmlns":579},[581,2370,2371,2395],{},[584,2372,2373,2375,2377,2379,2381,2387,2389,2391,2393],{},[723,2374,1082],{"stretchy":1295},[590,2376,804],{},[723,2378,731],{},[590,2380,734],{},[1303,2382,2383,2385],{},[723,2384,1096],{"stretchy":1295},[723,2386,1311],{"mathvariant":1309,"lspace":1310,"rspace":1310},[723,2388,1070],{},[590,2390,728],{},[723,2392,731],{},[590,2394,734],{},[598,2396,2397],{"encoding":600},"(\\cos x)' = \\sin x",[568,2399,2401,2463],{"className":2400,"ariaHidden":606},[605],[568,2402,2404,2408,2411,2414,2417,2420,2454,2457,2460],{"className":2403},[610],[568,2405],{"className":2406,"style":2407},[614],"height:1.0019em;vertical-align:-0.25em;",[568,2409,1082],{"className":2410},[623],[568,2412,804],{"className":2413},[759],[568,2415],{"className":2416,"style":755},[754],[568,2418,734],{"className":2419},[619,689],[568,2421,2423,2426],{"className":2422},[708],[568,2424,1096],{"className":2425},[708],[568,2427,2429],{"className":2428},[1380],[568,2430,2432],{"className":2431},[631],[568,2433,2435],{"className":2434},[636],[568,2436,2439],{"className":2437,"style":2438},[640],"height:0.7519em;",[568,2440,2442,2445],{"style":2441},"top:-3.063em;margin-right:0.05em;",[568,2443],{"className":2444,"style":1397},[648],[568,2446,2448],{"className":2447},[653,654,655,656],[568,2449,2451],{"className":2450},[619,656],[568,2452,1311],{"className":2453},[619,656],[568,2455],{"className":2456,"style":874},[754],[568,2458,1070],{"className":2459},[881],[568,2461],{"className":2462,"style":874},[754],[568,2464,2466,2469,2472,2475],{"className":2465},[610],[568,2467],{"className":2468,"style":861},[614],[568,2470,728],{"className":2471},[759],[568,2473],{"className":2474,"style":755},[754],[568,2476,734],{"className":2477},[619,689]," ist falsch.",[2358,2480,2481,2482,2612,2613,766],{},"Das Minus bei der zweiten Ableitung doppelt setzen: ",[568,2483,2485,2523],{"className":2484},[571],[568,2486,2488],{"className":2487},[575],[577,2489,2490],{"xmlns":579},[581,2491,2492,2520],{},[584,2493,2494,2496,2498,2500,2502,2504,2510,2512,2514,2516,2518],{},[723,2495,1082],{"stretchy":1295},[723,2497,725],{},[590,2499,728],{},[723,2501,731],{},[590,2503,734],{},[1303,2505,2506,2508],{},[723,2507,1096],{"stretchy":1295},[723,2509,1311],{"mathvariant":1309,"lspace":1310,"rspace":1310},[723,2511,1070],{},[723,2513,725],{},[590,2515,804],{},[723,2517,731],{},[590,2519,734],{},[598,2521,2522],{"encoding":600},"(-\\sin x)' = -\\cos x",[568,2524,2526,2591],{"className":2525,"ariaHidden":606},[605],[568,2527,2529,2532,2535,2538,2541,2544,2547,2550,2582,2585,2588],{"className":2528},[610],[568,2530],{"className":2531,"style":2407},[614],[568,2533,1082],{"className":2534},[623],[568,2536,725],{"className":2537},[619],[568,2539],{"className":2540,"style":755},[754],[568,2542,728],{"className":2543},[759],[568,2545],{"className":2546,"style":755},[754],[568,2548,734],{"className":2549},[619,689],[568,2551,2553,2556],{"className":2552},[708],[568,2554,1096],{"className":2555},[708],[568,2557,2559],{"className":2558},[1380],[568,2560,2562],{"className":2561},[631],[568,2563,2565],{"className":2564},[636],[568,2566,2568],{"className":2567,"style":2438},[640],[568,2569,2570,2573],{"style":2441},[568,2571],{"className":2572,"style":1397},[648],[568,2574,2576],{"className":2575},[653,654,655,656],[568,2577,2579],{"className":2578},[619,656],[568,2580,1311],{"className":2581},[619,656],[568,2583],{"className":2584,"style":874},[754],[568,2586,1070],{"className":2587},[881],[568,2589],{"className":2590,"style":874},[754],[568,2592,2594,2597,2600,2603,2606,2609],{"className":2593},[610],[568,2595],{"className":2596,"style":961},[614],[568,2598,725],{"className":2599},[619],[568,2601],{"className":2602,"style":755},[754],[568,2604,804],{"className":2605},[759],[568,2607],{"className":2608,"style":755},[754],[568,2610,734],{"className":2611},[619,689],", nicht ",[568,2614,2616,2634],{"className":2615},[571],[568,2617,2619],{"className":2618},[575],[577,2620,2621],{"xmlns":579},[581,2622,2623,2631],{},[584,2624,2625,2627,2629],{},[590,2626,804],{},[723,2628,731],{},[590,2630,734],{},[598,2632,2633],{"encoding":600},"\\cos x",[568,2635,2637],{"className":2636,"ariaHidden":606},[605],[568,2638,2640,2643,2646,2649],{"className":2639},[610],[568,2641],{"className":2642,"style":894},[614],[568,2644,804],{"className":2645},[759],[568,2647],{"className":2648,"style":755},[754],[568,2650,734],{"className":2651},[619,689],[2358,2653,2654,2655,2733,2734,2768],{},"Bei ",[568,2656,2658,2684],{"className":2657},[571],[568,2659,2661],{"className":2660},[575],[577,2662,2663],{"xmlns":579},[581,2664,2665,2681],{},[584,2666,2667,2669,2671,2673,2679],{},[590,2668,804],{},[723,2670,731],{},[723,2672,1082],{"stretchy":1295},[1303,2674,2675,2677],{},[590,2676,734],{},[594,2678,596],{},[723,2680,1096],{"stretchy":1295},[598,2682,2683],{"encoding":600},"\\cos(x^2)",[568,2685,2687],{"className":2686,"ariaHidden":606},[605],[568,2688,2690,2694,2697,2700,2730],{"className":2689},[610],[568,2691],{"className":2692,"style":2693},[614],"height:1.0641em;vertical-align:-0.25em;",[568,2695,804],{"className":2696},[759],[568,2698,1082],{"className":2699},[623],[568,2701,2703,2706],{"className":2702},[619],[568,2704,734],{"className":2705},[619,689],[568,2707,2709],{"className":2708},[1380],[568,2710,2712],{"className":2711},[631],[568,2713,2715],{"className":2714},[636],[568,2716,2719],{"className":2717,"style":2718},[640],"height:0.8141em;",[568,2720,2721,2724],{"style":2441},[568,2722],{"className":2723,"style":1397},[648],[568,2725,2727],{"className":2726},[653,654,655,656],[568,2728,596],{"className":2729},[619,656],[568,2731,1096],{"className":2732},[708]," die innere Ableitung ",[568,2735,2737,2753],{"className":2736},[571],[568,2738,2740],{"className":2739},[575],[577,2741,2742],{"xmlns":579},[581,2743,2744,2750],{},[584,2745,2746,2748],{},[594,2747,596],{},[590,2749,734],{},[598,2751,2752],{"encoding":600},"2x",[568,2754,2756],{"className":2755,"ariaHidden":606},[605],[568,2757,2759,2762,2765],{"className":2758},[610],[568,2760],{"className":2761,"style":1273},[614],[568,2763,596],{"className":2764},[619],[568,2766,734],{"className":2767},[619,689]," vergessen.",{"title":2770,"searchDepth":2771,"depth":2771,"links":2772},"",2,[2773,2774,2775,2776],{"id":561,"depth":2771,"text":562},{"id":1045,"depth":2771,"text":1046},{"id":1558,"depth":2771,"text":1559},{"id":2352,"depth":2771,"text":2353},[2778,2781,2784,2787,2790],{"lhs":2779,"rhs":2780},"round((cos(x+1e-5) - cos(x-1e-5))\u002F(2e-5) + sin(x), 6)","0",{"lhs":2782,"rhs":2783},"cos(x)","sin(x + pi\u002F2)",{"lhs":2785,"rhs":2786},"cos(x + pi\u002F2)","-sin(x)",{"lhs":2788,"rhs":2789},"-4*sin(pi\u002F2)","-4",{"lhs":2791,"rhs":2780},"round((cos((x+1e-5)^2) - cos((x-1e-5)^2))\u002F(2e-5) + 2*x*sin(x^2), 6)","x \\text{ im Bogenmaß}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">im Bogenmaß\u003C\u002Fspan>",null,"md","derivative-cosine","f(x) = \\cos x \\;\\Rightarrow\\; f'(x) = -\\sin x","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x) = \\cos x \\;\\Rightarrow\\; f'(x) = -\\sin x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0519em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7512em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord 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