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1",[574,1123,1125,1187],{"className":1124,"ariaHidden":595},[631],[574,1126,1128,1132,1169,1172,1175,1178,1181,1184],{"className":1127},[635],[574,1129],{"className":1130,"style":1131},[639],"height:1.0019em;vertical-align:-0.25em;",[574,1133,1135,1139],{"className":1134},[659],[574,1136,1101],{"className":1137,"style":1138},[659,731],"margin-right:0.1076em;",[574,1140,1143],{"className":1141},[1142],"msupsub",[574,1144,1146],{"className":1145},[673],[574,1147,1149],{"className":1148},[678],[574,1150,1153],{"className":1151,"style":1152},[682],"height:0.7519em;",[574,1154,1156,1160],{"style":1155},"top:-3.063em;margin-right:0.05em;",[574,1157],{"className":1158,"style":1159},[690],"height:2.7em;",[574,1161,1163],{"className":1162},[695,696,697,698],[574,1164,1166],{"className":1165},[659,698],[574,1167,1105],{"className":1168},[659,698],[574,1170,1108],{"className":1171},[648],[574,1173,1111],{"className":1174},[659],[574,1176,1114],{"className":1177},[750],[574,1179],{"className":1180,"style":944},[758],[574,1182,998],{"className":1183},[948],[574,1185],{"className":1186,"style":944},[758],[574,1188,1190,1193],{"className":1189},[635],[574,1191],{"className":1192,"style":977},[639],[574,1194,854],{"className":1195},[659],[565,1197,1198,1199,1202,1203,1373],{},"Für den ",[569,1200,1201],{},"Arkuskosinus"," gilt wegen ",[574,1204,1206,1243],{"className":1205},[577],[574,1207,1209],{"className":1208},[581],[583,1210,1211],{"xmlns":585},[587,1212,1213,1240],{},[590,1214,1215,1218,1221,1223,1225,1228,1230,1232,1234],{},[604,1216,1217],{},"arcsin",[593,1219,1220],{},"⁡",[604,1222,917],{},[593,1224,1056],{},[604,1226,1227],{},"arccos",[593,1229,1220],{},[604,1231,917],{},[593,1233,998],{},[601,1235,1236,1238],{},[604,1237,606],{},[608,1239,610],{},[624,1241,1242],{"encoding":626},"\\arcsin x + \\arccos x = \\frac{\\pi}{2}",[574,1244,1246,1274,1298],{"className":1245,"ariaHidden":595},[631],[574,1247,1249,1253,1257,1260,1263,1267,1271],{"className":1248},[635],[574,1250],{"className":1251,"style":1252},[639],"height:0.7512em;vertical-align:-0.0833em;",[574,1254,1217],{"className":1255},[1256],"mop",[574,1258],{"className":1259,"style":759},[758],[574,1261,917],{"className":1262},[659,731],[574,1264],{"className":1265,"style":1266},[758],"margin-right:0.2222em;",[574,1268,1056],{"className":1269},[1270],"mbin",[574,1272],{"className":1273,"style":1266},[758],[574,1275,1277,1280,1283,1286,1289,1292,1295],{"className":1276},[635],[574,1278],{"className":1279,"style":1016},[639],[574,1281,1227],{"className":1282},[1256],[574,1284],{"className":1285,"style":759},[758],[574,1287,917],{"className":1288},[659,731],[574,1290],{"className":1291,"style":944},[758],[574,1293,998],{"className":1294},[948],[574,1296],{"className":1297,"style":944},[758],[574,1299,1301,1305],{"className":1300},[635],[574,1302],{"className":1303,"style":1304},[639],"height:1.0404em;vertical-align:-0.345em;",[574,1306,1308,1311,1370],{"className":1307},[659],[574,1309],{"className":1310},[648,666],[574,1312,1314],{"className":1313},[601],[574,1315,1317,1362],{"className":1316},[673,674],[574,1318,1320,1359],{"className":1319},[678],[574,1321,1323,1337,1345],{"className":1322,"style":683},[682],[574,1324,1325,1328],{"style":686},[574,1326],{"className":1327,"style":691},[690],[574,1329,1331],{"className":1330},[695,696,697,698],[574,1332,1334],{"className":1333},[659,698],[574,1335,610],{"className":1336},[659,698],[574,1338,1339,1342],{"style":707},[574,1340],{"className":1341,"style":691},[690],[574,1343],{"className":1344,"style":715},[714],[574,1346,1347,1350],{"style":718},[574,1348],{"className":1349,"style":691},[690],[574,1351,1353],{"className":1352},[695,696,697,698],[574,1354,1356],{"className":1355},[659,698],[574,1357,606],{"className":1358,"style":732},[659,731,698],[574,1360,737],{"className":1361},[736],[574,1363,1365],{"className":1364},[678],[574,1366,1368],{"className":1367,"style":744},[682],[574,1369],{},[574,1371],{"className":1372},[750,666],":",[574,1375,1378],{"className":1376},[1377],"katex-display",[574,1379,1381,1431],{"className":1380},[577],[574,1382,1384],{"className":1383},[581],[583,1385,1387],{"xmlns":585,"display":1386},"block",[587,1388,1389,1428],{},[590,1390,1391,1393,1395,1397,1399,1405,1407,1409],{},[593,1392,1108],{"stretchy":849},[604,1394,1227],{},[593,1396,1220],{},[604,1398,917],{},[1097,1400,1401,1403],{},[593,1402,1114],{"stretchy":849},[593,1404,1105],{"mathvariant":1059,"lspace":1104,"rspace":1104},[593,1406,998],{},[593,1408,599],{},[601,1410,1411,1413],{},[608,1412,854],{},[1414,1415,1416],"msqrt",{},[590,1417,1418,1420,1422],{},[608,1419,854],{},[593,1421,599],{},[1097,1423,1424,1426],{},[604,1425,917],{},[608,1427,610],{},[624,1429,1430],{"encoding":626},"(\\arccos x)' = -\\frac{1}{\\sqrt{1 - x^2}}",[574,1432,1434,1496],{"className":1433,"ariaHidden":595},[631],[574,1435,1437,1441,1444,1447,1450,1453,1487,1490,1493],{"className":1436},[635],[574,1438],{"className":1439,"style":1440},[639],"height:1.0519em;vertical-align:-0.25em;",[574,1442,1108],{"className":1443},[648],[574,1445,1227],{"className":1446},[1256],[574,1448],{"className":1449,"style":759},[758],[574,1451,917],{"className":1452},[659,731],[574,1454,1456,1459],{"className":1455},[750],[574,1457,1114],{"className":1458},[750],[574,1460,1462],{"className":1461},[1142],[574,1463,1465],{"className":1464},[673],[574,1466,1468],{"className":1467},[678],[574,1469,1472],{"className":1470,"style":1471},[682],"height:0.8019em;",[574,1473,1475,1478],{"style":1474},"top:-3.113em;margin-right:0.05em;",[574,1476],{"className":1477,"style":1159},[690],[574,1479,1481],{"className":1480},[695,696,697,698],[574,1482,1484],{"className":1483},[659,698],[574,1485,1105],{"className":1486},[659,698],[574,1488],{"className":1489,"style":944},[758],[574,1491,998],{"className":1492},[948],[574,1494],{"className":1495,"style":944},[758],[574,1497,1499,1503,1506],{"className":1498},[635],[574,1500],{"className":1501,"style":1502},[639],"height:2.2514em;vertical-align:-0.93em;",[574,1504,599],{"className":1505},[659],[574,1507,1509,1512,1670],{"className":1508},[659],[574,1510],{"className":1511},[648,666],[574,1513,1515],{"className":1514},[601],[574,1516,1518,1661],{"className":1517},[673,674],[574,1519,1521,1658],{"className":1520},[678],[574,1522,1525,1638,1646],{"className":1523,"style":1524},[682],"height:1.3214em;",[574,1526,1528,1531],{"style":1527},"top:-2.1966em;",[574,1529],{"className":1530,"style":691},[690],[574,1532,1534],{"className":1533},[659],[574,1535,1538],{"className":1536},[659,1537],"sqrt",[574,1539,1541,1629],{"className":1540},[673,674],[574,1542,1544,1626],{"className":1543},[678],[574,1545,1548,1603],{"className":1546,"style":1547},[682],"height:0.9134em;",[574,1549,1553,1556],{"className":1550,"style":1552},[1551],"svg-align","top:-3em;",[574,1554],{"className":1555,"style":691},[690],[574,1557,1560,1563,1566,1569,1572],{"className":1558,"style":1559},[659],"padding-left:0.833em;",[574,1561,854],{"className":1562},[659],[574,1564],{"className":1565,"style":1266},[758],[574,1567,599],{"className":1568},[1270],[574,1570],{"className":1571,"style":1266},[758],[574,1573,1575,1578],{"className":1574},[659],[574,1576,917],{"className":1577},[659,731],[574,1579,1581],{"className":1580},[1142],[574,1582,1584],{"className":1583},[673],[574,1585,1587],{"className":1586},[678],[574,1588,1591],{"className":1589,"style":1590},[682],"height:0.7401em;",[574,1592,1594,1597],{"style":1593},"top:-2.989em;margin-right:0.05em;",[574,1595],{"className":1596,"style":1159},[690],[574,1598,1600],{"className":1599},[695,696,697,698],[574,1601,610],{"className":1602},[659,698],[574,1604,1606,1609],{"style":1605},"top:-2.8734em;",[574,1607],{"className":1608,"style":691},[690],[574,1610,1614],{"className":1611,"style":1613},[1612],"hide-tail","min-width:0.853em;height:1.08em;",[1615,1616,1622],"svg",{"xmlns":1617,"width":1618,"height":1619,"viewBox":1620,"preserveAspectRatio":1621},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1623,1624],"path",{"d":1625},"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",[574,1627,737],{"className":1628},[736],[574,1630,1632],{"className":1631},[678],[574,1633,1636],{"className":1634,"style":1635},[682],"height:0.1266em;",[574,1637],{},[574,1639,1640,1643],{"style":707},[574,1641],{"className":1642,"style":691},[690],[574,1644],{"className":1645,"style":715},[714],[574,1647,1649,1652],{"style":1648},"top:-3.677em;",[574,1650],{"className":1651,"style":691},[690],[574,1653,1655],{"className":1654},[659],[574,1656,854],{"className":1657},[659],[574,1659,737],{"className":1660},[736],[574,1662,1664],{"className":1663},[678],[574,1665,1668],{"className":1666,"style":1667},[682],"height:0.93em;",[574,1669],{},[574,1671],{"className":1672},[750,666],[560,1674,1676],{"id":1675},"herleitung","Herleitung",[565,1678,1679,1680,1744,1745,1373],{},"Mit der Ableitung der Umkehrfunktion und ",[574,1681,1683,1706],{"className":1682},[577],[574,1684,1686],{"className":1685},[581],[583,1687,1688],{"xmlns":585},[587,1689,1690,1703],{},[590,1691,1692,1695,1697,1699,1701],{},[604,1693,1694],{},"y",[593,1696,998],{},[604,1698,1217],{},[593,1700,1220],{},[604,1702,917],{},[624,1704,1705],{"encoding":626},"y = \\arcsin x",[574,1707,1709,1728],{"className":1708,"ariaHidden":595},[631],[574,1710,1712,1716,1719,1722,1725],{"className":1711},[635],[574,1713],{"className":1714,"style":1715},[639],"height:0.625em;vertical-align:-0.1944em;",[574,1717,1694],{"className":1718,"style":732},[659,731],[574,1720],{"className":1721,"style":944},[758],[574,1723,998],{"className":1724},[948],[574,1726],{"className":1727,"style":944},[758],[574,1729,1731,1735,1738,1741],{"className":1730},[635],[574,1732],{"className":1733,"style":1734},[639],"height:0.6679em;",[574,1736,1217],{"className":1737},[1256],[574,1739],{"className":1740,"style":759},[758],[574,1742,917],{"className":1743},[659,731],", also ",[574,1746,1748,1771],{"className":1747},[577],[574,1749,1751],{"className":1750},[581],[583,1752,1753],{"xmlns":585},[587,1754,1755,1768],{},[590,1756,1757,1760,1762,1764,1766],{},[604,1758,1759],{},"sin",[593,1761,1220],{},[604,1763,1694],{},[593,1765,998],{},[604,1767,917],{},[624,1769,1770],{"encoding":626},"\\sin y = x",[574,1772,1774,1799],{"className":1773,"ariaHidden":595},[631],[574,1775,1777,1781,1784,1787,1790,1793,1796],{"className":1776},[635],[574,1778],{"className":1779,"style":1780},[639],"height:0.8623em;vertical-align:-0.1944em;",[574,1782,1759],{"className":1783},[1256],[574,1785],{"className":1786,"style":759},[758],[574,1788,1694],{"className":1789,"style":732},[659,731],[574,1791],{"className":1792,"style":944},[758],[574,1794,998],{"className":1795},[948],[574,1797],{"className":1798,"style":944},[758],[574,1800,1802,1805],{"className":1801},[635],[574,1803],{"className":1804,"style":1016},[639],[574,1806,917],{"className":1807},[659,731],[574,1809,1811],{"className":1810},[1377],[574,1812,1814,1901],{"className":1813},[577],[574,1815,1817],{"className":1816},[581],[583,1818,1819],{"xmlns":585,"display":1386},[587,1820,1821,1898],{},[590,1822,1823,1825,1827,1829,1831,1837,1839,1852,1854,1878,1880],{},[593,1824,1108],{"stretchy":849},[604,1826,1217],{},[593,1828,1220],{},[604,1830,917],{},[1097,1832,1833,1835],{},[593,1834,1114],{"stretchy":849},[593,1836,1105],{"mathvariant":1059,"lspace":1104,"rspace":1104},[593,1838,998],{},[601,1840,1841,1843],{},[608,1842,854],{},[590,1844,1845,1848,1850],{},[604,1846,1847],{},"cos",[593,1849,1220],{},[604,1851,1694],{},[593,1853,998],{},[601,1855,1856,1858],{},[608,1857,854],{},[1414,1859,1860],{},[590,1861,1862,1864,1866,1876],{},[608,1863,854],{},[593,1865,599],{},[1097,1867,1868,1874],{},[590,1869,1870,1872],{},[604,1871,1759],{},[593,1873,1220],{},[608,1875,610],{},[604,1877,1694],{},[593,1879,998],{},[601,1881,1882,1884],{},[608,1883,854],{},[1414,1885,1886],{},[590,1887,1888,1890,1892],{},[608,1889,854],{},[593,1891,599],{},[1097,1893,1894,1896],{},[604,1895,917],{},[608,1897,610],{},[624,1899,1900],{"encoding":626},"(\\arcsin x)' = \\frac{1}{\\cos y} = \\frac{1}{\\sqrt{1 - \\sin^2 y}} = \\frac{1}{\\sqrt{1 - x^2}}",[574,1902,1904,1963,2049,2232],{"className":1903,"ariaHidden":595},[631],[574,1905,1907,1910,1913,1916,1919,1922,1954,1957,1960],{"className":1906},[635],[574,1908],{"className":1909,"style":1440},[639],[574,1911,1108],{"className":1912},[648],[574,1914,1217],{"className":1915},[1256],[574,1917],{"className":1918,"style":759},[758],[574,1920,917],{"className":1921},[659,731],[574,1923,1925,1928],{"className":1924},[750],[574,1926,1114],{"className":1927},[750],[574,1929,1931],{"className":1930},[1142],[574,1932,1934],{"className":1933},[673],[574,1935,1937],{"className":1936},[678],[574,1938,1940],{"className":1939,"style":1471},[682],[574,1941,1942,1945],{"style":1474},[574,1943],{"className":1944,"style":1159},[690],[574,1946,1948],{"className":1947},[695,696,697,698],[574,1949,1951],{"className":1950},[659,698],[574,1952,1105],{"className":1953},[659,698],[574,1955],{"className":1956,"style":944},[758],[574,1958,998],{"className":1959},[948],[574,1961],{"className":1962,"style":944},[758],[574,1964,1966,1970,2040,2043,2046],{"className":1965},[635],[574,1967],{"className":1968,"style":1969},[639],"height:2.2019em;vertical-align:-0.8804em;",[574,1971,1973,1976,2037],{"className":1972},[659],[574,1974],{"className":1975},[648,666],[574,1977,1979],{"className":1978},[601],[574,1980,1982,2028],{"className":1981},[673,674],[574,1983,1985,2025],{"className":1984},[678],[574,1986,1988,2006,2014],{"className":1987,"style":1524},[682],[574,1989,1991,1994],{"style":1990},"top:-2.314em;",[574,1992],{"className":1993,"style":691},[690],[574,1995,1997,2000,2003],{"className":1996},[659],[574,1998,1847],{"className":1999},[1256],[574,2001],{"className":2002,"style":759},[758],[574,2004,1694],{"className":2005,"style":732},[659,731],[574,2007,2008,2011],{"style":707},[574,2009],{"className":2010,"style":691},[690],[574,2012],{"className":2013,"style":715},[714],[574,2015,2016,2019],{"style":1648},[574,2017],{"className":2018,"style":691},[690],[574,2020,2022],{"className":2021},[659],[574,2023,854],{"className":2024},[659],[574,2026,737],{"className":2027},[736],[574,2029,2031],{"className":2030},[678],[574,2032,2035],{"className":2033,"style":2034},[682],"height:0.8804em;",[574,2036],{},[574,2038],{"className":2039},[750,666],[574,2041],{"className":2042,"style":944},[758],[574,2044,998],{"className":2045},[948],[574,2047],{"className":2048,"style":944},[758],[574,2050,2052,2056,2223,2226,2229],{"className":2051},[635],[574,2053],{"className":2054,"style":2055},[639],"height:2.4514em;vertical-align:-1.13em;",[574,2057,2059,2062,2220],{"className":2058},[659],[574,2060],{"className":2061},[648,666],[574,2063,2065],{"className":2064},[601],[574,2066,2068,2211],{"className":2067},[673,674],[574,2069,2071,2208],{"className":2070},[678],[574,2072,2074,2187,2196],{"className":2073,"style":1524},[682],[574,2075,2077,2081],{"style":2076},"top:-2.11em;",[574,2078],{"className":2079,"style":2080},[690],"height:3.0237em;",[574,2082,2084],{"className":2083},[659],[574,2085,2087],{"className":2086},[659,1537],[574,2088,2090,2178],{"className":2089},[673,674],[574,2091,2093,2175],{"className":2092},[678],[574,2094,2097,2158],{"className":2095,"style":2096},[682],"height:1.0237em;",[574,2098,2101,2105],{"className":2099,"style":2100},[1551],"top:-3.2em;",[574,2102],{"className":2103,"style":2104},[690],"height:3.2em;",[574,2106,2109,2112,2115,2118,2121,2152,2155],{"className":2107,"style":2108},[659],"padding-left:1em;",[574,2110,854],{"className":2111},[659],[574,2113],{"className":2114,"style":1266},[758],[574,2116,599],{"className":2117},[1270],[574,2119],{"className":2120,"style":1266},[758],[574,2122,2124,2127],{"className":2123},[1256],[574,2125,1759],{"className":2126},[1256],[574,2128,2130],{"className":2129},[1142],[574,2131,2133],{"className":2132},[673],[574,2134,2136],{"className":2135},[678],[574,2137,2140],{"className":2138,"style":2139},[682],"height:0.8719em;",[574,2141,2143,2146],{"style":2142},"top:-3.1208em;margin-right:0.05em;",[574,2144],{"className":2145,"style":1159},[690],[574,2147,2149],{"className":2148},[695,696,697,698],[574,2150,610],{"className":2151},[659,698],[574,2153],{"className":2154,"style":759},[758],[574,2156,1694],{"className":2157,"style":732},[659,731],[574,2159,2161,2164],{"style":2160},"top:-2.9837em;",[574,2162],{"className":2163,"style":2104},[690],[574,2165,2168],{"className":2166,"style":2167},[1612],"min-width:1.02em;height:1.28em;",[1615,2169,2172],{"xmlns":1617,"width":1618,"height":2170,"viewBox":2171,"preserveAspectRatio":1621},"1.28em","0 0 400000 1296",[1623,2173],{"d":2174},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[574,2176,737],{"className":2177},[736],[574,2179,2181],{"className":2180},[678],[574,2182,2185],{"className":2183,"style":2184},[682],"height:0.2163em;",[574,2186],{},[574,2188,2190,2193],{"style":2189},"top:-3.2537em;",[574,2191],{"className":2192,"style":2080},[690],[574,2194],{"className":2195,"style":715},[714],[574,2197,2199,2202],{"style":2198},"top:-3.7007em;",[574,2200],{"className":2201,"style":2080},[690],[574,2203,2205],{"className":2204},[659],[574,2206,854],{"className":2207},[659],[574,2209,737],{"className":2210},[736],[574,2212,2214],{"className":2213},[678],[574,2215,2218],{"className":2216,"style":2217},[682],"height:1.13em;",[574,2219],{},[574,2221],{"className":2222},[750,666],[574,2224],{"className":2225,"style":944},[758],[574,2227,998],{"className":2228},[948],[574,2230],{"className":2231,"style":944},[758],[574,2233,2235,2238],{"className":2234},[635],[574,2236],{"className":2237,"style":1502},[639],[574,2239,2241,2244,2379],{"className":2240},[659],[574,2242],{"className":2243},[648,666],[574,2245,2247],{"className":2246},[601],[574,2248,2250,2371],{"className":2249},[673,674],[574,2251,2253,2368],{"className":2252},[678],[574,2254,2256,2349,2357],{"className":2255,"style":1524},[682],[574,2257,2258,2261],{"style":1527},[574,2259],{"className":2260,"style":691},[690],[574,2262,2264],{"className":2263},[659],[574,2265,2267],{"className":2266},[659,1537],[574,2268,2270,2341],{"className":2269},[673,674],[574,2271,2273,2338],{"className":2272},[678],[574,2274,2276,2326],{"className":2275,"style":1547},[682],[574,2277,2279,2282],{"className":2278,"style":1552},[1551],[574,2280],{"className":2281,"style":691},[690],[574,2283,2285,2288,2291,2294,2297],{"className":2284,"style":1559},[659],[574,2286,854],{"className":2287},[659],[574,2289],{"className":2290,"style":1266},[758],[574,2292,599],{"className":2293},[1270],[574,2295],{"className":2296,"style":1266},[758],[574,2298,2300,2303],{"className":2299},[659],[574,2301,917],{"className":2302},[659,731],[574,2304,2306],{"className":2305},[1142],[574,2307,2309],{"className":2308},[673],[574,2310,2312],{"className":2311},[678],[574,2313,2315],{"className":2314,"style":1590},[682],[574,2316,2317,2320],{"style":1593},[574,2318],{"className":2319,"style":1159},[690],[574,2321,2323],{"className":2322},[695,696,697,698],[574,2324,610],{"className":2325},[659,698],[574,2327,2328,2331],{"style":1605},[574,2329],{"className":2330,"style":691},[690],[574,2332,2334],{"className":2333,"style":1613},[1612],[1615,2335,2336],{"xmlns":1617,"width":1618,"height":1619,"viewBox":1620,"preserveAspectRatio":1621},[1623,2337],{"d":1625},[574,2339,737],{"className":2340},[736],[574,2342,2344],{"className":2343},[678],[574,2345,2347],{"className":2346,"style":1635},[682],[574,2348],{},[574,2350,2351,2354],{"style":707},[574,2352],{"className":2353,"style":691},[690],[574,2355],{"className":2356,"style":715},[714],[574,2358,2359,2362],{"style":1648},[574,2360],{"className":2361,"style":691},[690],[574,2363,2365],{"className":2364},[659],[574,2366,854],{"className":2367},[659],[574,2369,737],{"className":2370},[736],[574,2372,2374],{"className":2373},[678],[574,2375,2377],{"className":2376,"style":1667},[682],[574,2378],{},[574,2380],{"className":2381},[750,666],[565,2383,2384,2385,2413,2414,2517,2518,2616],{},"Die positive Wurzel ist richtig, weil ",[574,2386,2388,2401],{"className":2387},[577],[574,2389,2391],{"className":2390},[581],[583,2392,2393],{"xmlns":585},[587,2394,2395,2399],{},[590,2396,2397],{},[604,2398,1694],{},[624,2400,1694],{"encoding":626},[574,2402,2404],{"className":2403,"ariaHidden":595},[631],[574,2405,2407,2410],{"className":2406},[635],[574,2408],{"className":2409,"style":1715},[639],[574,2411,1694],{"className":2412,"style":732},[659,731]," zwischen ",[574,2415,2417,2437],{"className":2416},[577],[574,2418,2420],{"className":2419},[581],[583,2421,2422],{"xmlns":585},[587,2423,2424,2434],{},[590,2425,2426,2428],{},[593,2427,599],{},[601,2429,2430,2432],{},[604,2431,606],{},[608,2433,610],{},[624,2435,2436],{"encoding":626},"-\\frac{\\pi}{2}",[574,2438,2440],{"className":2439,"ariaHidden":595},[631],[574,2441,2443,2446,2449],{"className":2442},[635],[574,2444],{"className":2445,"style":1304},[639],[574,2447,599],{"className":2448},[659],[574,2450,2452,2455,2514],{"className":2451},[659],[574,2453],{"className":2454},[648,666],[574,2456,2458],{"className":2457},[601],[574,2459,2461,2506],{"className":2460},[673,674],[574,2462,2464,2503],{"className":2463},[678],[574,2465,2467,2481,2489],{"className":2466,"style":683},[682],[574,2468,2469,2472],{"style":686},[574,2470],{"className":2471,"style":691},[690],[574,2473,2475],{"className":2474},[695,696,697,698],[574,2476,2478],{"className":2477},[659,698],[574,2479,610],{"className":2480},[659,698],[574,2482,2483,2486],{"style":707},[574,2484],{"className":2485,"style":691},[690],[574,2487],{"className":2488,"style":715},[714],[574,2490,2491,2494],{"style":718},[574,2492],{"className":2493,"style":691},[690],[574,2495,2497],{"className":2496},[695,696,697,698],[574,2498,2500],{"className":2499},[659,698],[574,2501,606],{"className":2502,"style":732},[659,731,698],[574,2504,737],{"className":2505},[736],[574,2507,2509],{"className":2508},[678],[574,2510,2512],{"className":2511,"style":744},[682],[574,2513],{},[574,2515],{"className":2516},[750,666]," und ",[574,2519,2521,2539],{"className":2520},[577],[574,2522,2524],{"className":2523},[581],[583,2525,2526],{"xmlns":585},[587,2527,2528,2536],{},[590,2529,2530],{},[601,2531,2532,2534],{},[604,2533,606],{},[608,2535,610],{},[624,2537,2538],{"encoding":626},"\\frac{\\pi}{2}",[574,2540,2542],{"className":2541,"ariaHidden":595},[631],[574,2543,2545,2548],{"className":2544},[635],[574,2546],{"className":2547,"style":1304},[639],[574,2549,2551,2554,2613],{"className":2550},[659],[574,2552],{"className":2553},[648,666],[574,2555,2557],{"className":2556},[601],[574,2558,2560,2605],{"className":2559},[673,674],[574,2561,2563,2602],{"className":2562},[678],[574,2564,2566,2580,2588],{"className":2565,"style":683},[682],[574,2567,2568,2571],{"style":686},[574,2569],{"className":2570,"style":691},[690],[574,2572,2574],{"className":2573},[695,696,697,698],[574,2575,2577],{"className":2576},[659,698],[574,2578,610],{"className":2579},[659,698],[574,2581,2582,2585],{"style":707},[574,2583],{"className":2584,"style":691},[690],[574,2586],{"className":2587,"style":715},[714],[574,2589,2590,2593],{"style":718},[574,2591],{"className":2592,"style":691},[690],[574,2594,2596],{"className":2595},[695,696,697,698],[574,2597,2599],{"className":2598},[659,698],[574,2600,606],{"className":2601,"style":732},[659,731,698],[574,2603,737],{"className":2604},[736],[574,2606,2608],{"className":2607},[678],[574,2609,2611],{"className":2610,"style":744},[682],[574,2612],{},[574,2614],{"className":2615},[750,666]," liegt und der Kosinus dort nicht negativ ist.",[560,2618,2620],{"id":2619},"beispiele","Beispiele",[565,2622,2623,2624,2517,2675,1373],{},"An den Stellen ",[574,2625,2627,2645],{"className":2626},[577],[574,2628,2630],{"className":2629},[581],[583,2631,2632],{"xmlns":585},[587,2633,2634,2642],{},[590,2635,2636,2638,2640],{},[604,2637,917],{},[593,2639,998],{},[608,2641,1111],{},[624,2643,2644],{"encoding":626},"x = 0",[574,2646,2648,2666],{"className":2647,"ariaHidden":595},[631],[574,2649,2651,2654,2657,2660,2663],{"className":2650},[635],[574,2652],{"className":2653,"style":1016},[639],[574,2655,917],{"className":2656},[659,731],[574,2658],{"className":2659,"style":944},[758],[574,2661,998],{"className":2662},[948],[574,2664],{"className":2665,"style":944},[758],[574,2667,2669,2672],{"className":2668},[635],[574,2670],{"className":2671,"style":977},[639],[574,2673,1111],{"className":2674},[659],[574,2676,2678,2697],{"className":2677},[577],[574,2679,2681],{"className":2680},[581],[583,2682,2683],{"xmlns":585},[587,2684,2685,2694],{},[590,2686,2687,2689,2691],{},[604,2688,917],{},[593,2690,998],{},[608,2692,2693],{},"0,5",[624,2695,2696],{"encoding":626},"x = 0{,}5",[574,2698,2700,2718],{"className":2699,"ariaHidden":595},[631],[574,2701,2703,2706,2709,2712,2715],{"className":2702},[635],[574,2704],{"className":2705,"style":1016},[639],[574,2707,917],{"className":2708},[659,731],[574,2710],{"className":2711,"style":944},[758],[574,2713,998],{"className":2714},[948],[574,2716],{"className":2717,"style":944},[758],[574,2719,2721,2725,2728,2734],{"className":2720},[635],[574,2722],{"className":2723,"style":2724},[639],"height:0.8389em;vertical-align:-0.1944em;",[574,2726,1111],{"className":2727},[659],[574,2729,2731],{"className":2730},[659],[574,2732,613],{"className":2733},[754],[574,2735,2737],{"className":2736},[659],"5",[574,2739,2741],{"className":2740},[1377],[574,2742,2744,2827],{"className":2743},[577],[574,2745,2747],{"className":2746},[581],[583,2748,2749],{"xmlns":585,"display":1386},[587,2750,2751,2824],{},[590,2752,2753,2759,2761,2763,2765,2767,2775,2777,2779,2781,2784,2790,2792,2794,2796,2798,2807,2809,2818,2821],{},[1097,2754,2755,2757],{},[604,2756,1101],{},[593,2758,1105],{"mathvariant":1059,"lspace":1104,"rspace":1104},[593,2760,1108],{"stretchy":849},[608,2762,1111],{},[593,2764,1114],{"stretchy":849},[593,2766,998],{},[601,2768,2769,2771],{},[608,2770,854],{},[1414,2772,2773],{},[608,2774,854],{},[593,2776,998],{},[608,2778,854],{},[593,2780,613],{"separator":595},[758,2782],{"width":2783},"2em",[1097,2785,2786,2788],{},[604,2787,1101],{},[593,2789,1105],{"mathvariant":1059,"lspace":1104,"rspace":1104},[593,2791,1108],{"stretchy":849},[608,2793,2693],{},[593,2795,1114],{"stretchy":849},[593,2797,998],{},[601,2799,2800,2802],{},[608,2801,854],{},[1414,2803,2804],{},[608,2805,2806],{},"0,75",[593,2808,998],{},[601,2810,2811,2813],{},[608,2812,610],{},[1414,2814,2815],{},[608,2816,2817],{},"3",[593,2819,2820],{},"≈",[608,2822,2823],{},"1,1547",[624,2825,2826],{"encoding":626},"f'(0) = \\frac{1}{\\sqrt{1}} = 1, \\qquad f'(0{,}5) = \\frac{1}{\\sqrt{0{,}75}} = \\frac{2}{\\sqrt{3}} \\approx 1{,}1547",[574,2828,2830,2886,3011,3089,3224,3345],{"className":2829,"ariaHidden":595},[631],[574,2831,2833,2836,2868,2871,2874,2877,2880,2883],{"className":2832},[635],[574,2834],{"className":2835,"style":1440},[639],[574,2837,2839,2842],{"className":2838},[659],[574,2840,1101],{"className":2841,"style":1138},[659,731],[574,2843,2845],{"className":2844},[1142],[574,2846,2848],{"className":2847},[673],[574,2849,2851],{"className":2850},[678],[574,2852,2854],{"className":2853,"style":1471},[682],[574,2855,2856,2859],{"style":1474},[574,2857],{"className":2858,"style":1159},[690],[574,2860,2862],{"className":2861},[695,696,697,698],[574,2863,2865],{"className":2864},[659,698],[574,2866,1105],{"className":2867},[659,698],[574,2869,1108],{"className":2870},[648],[574,2872,1111],{"className":2873},[659],[574,2875,1114],{"className":2876},[750],[574,2878],{"className":2879,"style":944},[758],[574,2881,998],{"className":2882},[948],[574,2884],{"className":2885,"style":944},[758],[574,2887,2889,2892,3002,3005,3008],{"className":2888},[635],[574,2890],{"className":2891,"style":1502},[639],[574,2893,2895,2898,2999],{"className":2894},[659],[574,2896],{"className":2897},[648,666],[574,2899,2901],{"className":2900},[601],[574,2902,2904,2991],{"className":2903},[673,674],[574,2905,2907,2988],{"className":2906},[678],[574,2908,2910,2969,2977],{"className":2909,"style":1524},[682],[574,2911,2913,2916],{"style":2912},"top:-2.2028em;",[574,2914],{"className":2915,"style":691},[690],[574,2917,2919],{"className":2918},[659],[574,2920,2922],{"className":2921},[659,1537],[574,2923,2925,2960],{"className":2924},[673,674],[574,2926,2928,2957],{"className":2927},[678],[574,2929,2932,2944],{"className":2930,"style":2931},[682],"height:0.9072em;",[574,2933,2935,2938],{"className":2934,"style":1552},[1551],[574,2936],{"className":2937,"style":691},[690],[574,2939,2941],{"className":2940,"style":1559},[659],[574,2942,854],{"className":2943},[659],[574,2945,2947,2950],{"style":2946},"top:-2.8672em;",[574,2948],{"className":2949,"style":691},[690],[574,2951,2953],{"className":2952,"style":1613},[1612],[1615,2954,2955],{"xmlns":1617,"width":1618,"height":1619,"viewBox":1620,"preserveAspectRatio":1621},[1623,2956],{"d":1625},[574,2958,737],{"className":2959},[736],[574,2961,2963],{"className":2962},[678],[574,2964,2967],{"className":2965,"style":2966},[682],"height:0.1328em;",[574,2968],{},[574,2970,2971,2974],{"style":707},[574,2972],{"className":2973,"style":691},[690],[574,2975],{"className":2976,"style":715},[714],[574,2978,2979,2982],{"style":1648},[574,2980],{"className":2981,"style":691},[690],[574,2983,2985],{"className":2984},[659],[574,2986,854],{"className":2987},[659],[574,2989,737],{"className":2990},[736],[574,2992,2994],{"className":2993},[678],[574,2995,2997],{"className":2996,"style":1667},[682],[574,2998],{},[574,3000],{"className":3001},[750,666],[574,3003],{"className":3004,"style":944},[758],[574,3006,998],{"className":3007},[948],[574,3009],{"className":3010,"style":944},[758],[574,3012,3014,3017,3020,3023,3027,3030,3062,3065,3068,3074,3077,3080,3083,3086],{"className":3013},[635],[574,3015],{"className":3016,"style":1440},[639],[574,3018,854],{"className":3019},[659],[574,3021,613],{"className":3022},[754],[574,3024],{"className":3025,"style":3026},[758],"margin-right:2em;",[574,3028],{"className":3029,"style":759},[758],[574,3031,3033,3036],{"className":3032},[659],[574,3034,1101],{"className":3035,"style":1138},[659,731],[574,3037,3039],{"className":3038},[1142],[574,3040,3042],{"className":3041},[673],[574,3043,3045],{"className":3044},[678],[574,3046,3048],{"className":3047,"style":1471},[682],[574,3049,3050,3053],{"style":1474},[574,3051],{"className":3052,"style":1159},[690],[574,3054,3056],{"className":3055},[695,696,697,698],[574,3057,3059],{"className":3058},[659,698],[574,3060,1105],{"className":3061},[659,698],[574,3063,1108],{"className":3064},[648],[574,3066,1111],{"className":3067},[659],[574,3069,3071],{"className":3070},[659],[574,3072,613],{"className":3073},[754],[574,3075,2737],{"className":3076},[659],[574,3078,1114],{"className":3079},[750],[574,3081],{"className":3082,"style":944},[758],[574,3084,998],{"className":3085},[948],[574,3087],{"className":3088,"style":944},[758],[574,3090,3092,3095,3215,3218,3221],{"className":3091},[635],[574,3093],{"className":3094,"style":1502},[639],[574,3096,3098,3101,3212],{"className":3097},[659],[574,3099],{"className":3100},[648,666],[574,3102,3104],{"className":3103},[601],[574,3105,3107,3204],{"className":3106},[673,674],[574,3108,3110,3201],{"className":3109},[678],[574,3111,3113,3182,3190],{"className":3112,"style":1524},[682],[574,3114,3116,3119],{"style":3115},"top:-2.3em;",[574,3117],{"className":3118,"style":691},[690],[574,3120,3122],{"className":3121},[659],[574,3123,3125],{"className":3124},[659,1537],[574,3126,3128,3173],{"className":3127},[673,674],[574,3129,3131,3170],{"className":3130},[678],[574,3132,3135,3157],{"className":3133,"style":3134},[682],"height:0.81em;",[574,3136,3138,3141],{"className":3137,"style":1552},[1551],[574,3139],{"className":3140,"style":691},[690],[574,3142,3144,3147,3153],{"className":3143,"style":1559},[659],[574,3145,1111],{"className":3146},[659],[574,3148,3150],{"className":3149},[659],[574,3151,613],{"className":3152},[754],[574,3154,3156],{"className":3155},[659],"75",[574,3158,3160,3163],{"style":3159},"top:-2.77em;",[574,3161],{"className":3162,"style":691},[690],[574,3164,3166],{"className":3165,"style":1613},[1612],[1615,3167,3168],{"xmlns":1617,"width":1618,"height":1619,"viewBox":1620,"preserveAspectRatio":1621},[1623,3169],{"d":1625},[574,3171,737],{"className":3172},[736],[574,3174,3176],{"className":3175},[678],[574,3177,3180],{"className":3178,"style":3179},[682],"height:0.23em;",[574,3181],{},[574,3183,3184,3187],{"style":707},[574,3185],{"className":3186,"style":691},[690],[574,3188],{"className":3189,"style":715},[714],[574,3191,3192,3195],{"style":1648},[574,3193],{"className":3194,"style":691},[690],[574,3196,3198],{"className":3197},[659],[574,3199,854],{"className":3200},[659],[574,3202,737],{"className":3203},[736],[574,3205,3207],{"className":3206},[678],[574,3208,3210],{"className":3209,"style":1667},[682],[574,3211],{},[574,3213],{"className":3214},[750,666],[574,3216],{"className":3217,"style":944},[758],[574,3219,998],{"className":3220},[948],[574,3222],{"className":3223,"style":944},[758],[574,3225,3227,3230,3336,3339,3342],{"className":3226},[635],[574,3228],{"className":3229,"style":1502},[639],[574,3231,3233,3236,3333],{"className":3232},[659],[574,3234],{"className":3235},[648,666],[574,3237,3239],{"className":3238},[601],[574,3240,3242,3325],{"className":3241},[673,674],[574,3243,3245,3322],{"className":3244},[678],[574,3246,3248,3303,3311],{"className":3247,"style":1524},[682],[574,3249,3250,3253],{"style":2912},[574,3251],{"className":3252,"style":691},[690],[574,3254,3256],{"className":3255},[659],[574,3257,3259],{"className":3258},[659,1537],[574,3260,3262,3295],{"className":3261},[673,674],[574,3263,3265,3292],{"className":3264},[678],[574,3266,3268,3280],{"className":3267,"style":2931},[682],[574,3269,3271,3274],{"className":3270,"style":1552},[1551],[574,3272],{"className":3273,"style":691},[690],[574,3275,3277],{"className":3276,"style":1559},[659],[574,3278,2817],{"className":3279},[659],[574,3281,3282,3285],{"style":2946},[574,3283],{"className":3284,"style":691},[690],[574,3286,3288],{"className":3287,"style":1613},[1612],[1615,3289,3290],{"xmlns":1617,"width":1618,"height":1619,"viewBox":1620,"preserveAspectRatio":1621},[1623,3291],{"d":1625},[574,3293,737],{"className":3294},[736],[574,3296,3298],{"className":3297},[678],[574,3299,3301],{"className":3300,"style":2966},[682],[574,3302],{},[574,3304,3305,3308],{"style":707},[574,3306],{"className":3307,"style":691},[690],[574,3309],{"className":3310,"style":715},[714],[574,3312,3313,3316],{"style":1648},[574,3314],{"className":3315,"style":691},[690],[574,3317,3319],{"className":3318},[659],[574,3320,610],{"className":3321},[659],[574,3323,737],{"className":3324},[736],[574,3326,3328],{"className":3327},[678],[574,3329,3331],{"className":3330,"style":1667},[682],[574,3332],{},[574,3334],{"className":3335},[750,666],[574,3337],{"className":3338,"style":944},[758],[574,3340,2820],{"className":3341},[948],[574,3343],{"className":3344,"style":944},[758],[574,3346,3348,3351,3354,3360],{"className":3347},[635],[574,3349],{"className":3350,"style":2724},[639],[574,3352,854],{"className":3353},[659],[574,3355,3357],{"className":3356},[659],[574,3358,613],{"className":3359},[754],[574,3361,3363],{"className":3362},[659],"1547",[565,3365,3366,3367,1373],{},"Mit der Kettenregel, innere Ableitung ",[574,3368,3370,3383],{"className":3369},[577],[574,3371,3373],{"className":3372},[581],[583,3374,3375],{"xmlns":585},[587,3376,3377,3381],{},[590,3378,3379],{},[608,3380,610],{},[624,3382,610],{"encoding":626},[574,3384,3386],{"className":3385,"ariaHidden":595},[631],[574,3387,3389,3392],{"className":3388},[635],[574,3390],{"className":3391,"style":977},[639],[574,3393,610],{"className":3394},[659],[574,3396,3398],{"className":3397},[1377],[574,3399,3401,3513],{"className":3400},[577],[574,3402,3404],{"className":3403},[581],[583,3405,3406],{"xmlns":585,"display":1386},[587,3407,3408,3510],{},[590,3409,3410,3413,3415,3417,3419,3421,3423,3425,3427,3429,3431,3433,3437,3440,3442,3448,3450,3452,3454,3456,3477,3479,3481,3487,3489,3492,3494,3496,3505,3507],{},[604,3411,3412],{},"g",[593,3414,1108],{"stretchy":849},[604,3416,917],{},[593,3418,1114],{"stretchy":849},[593,3420,998],{},[604,3422,1217],{},[593,3424,1220],{},[593,3426,1108],{"stretchy":849},[608,3428,610],{},[604,3430,917],{},[593,3432,1114],{"stretchy":849},[3434,3435,3436],"mtext",{},"  ",[593,3438,3439],{},"⇒",[3434,3441,3436],{},[1097,3443,3444,3446],{},[604,3445,3412],{},[593,3447,1105],{"mathvariant":1059,"lspace":1104,"rspace":1104},[593,3449,1108],{"stretchy":849},[604,3451,917],{},[593,3453,1114],{"stretchy":849},[593,3455,998],{},[601,3457,3458,3460],{},[608,3459,610],{},[1414,3461,3462],{},[590,3463,3464,3466,3468,3471],{},[608,3465,854],{},[593,3467,599],{},[608,3469,3470],{},"4",[1097,3472,3473,3475],{},[604,3474,917],{},[608,3476,610],{},[593,3478,613],{"separator":595},[758,3480],{"width":2783},[1097,3482,3483,3485],{},[604,3484,3412],{},[593,3486,1105],{"mathvariant":1059,"lspace":1104,"rspace":1104},[593,3488,1108],{"stretchy":849},[608,3490,3491],{},"0,3",[593,3493,1114],{"stretchy":849},[593,3495,998],{},[601,3497,3498,3500],{},[608,3499,610],{},[1414,3501,3502],{},[608,3503,3504],{},"0,64",[593,3506,998],{},[608,3508,3509],{},"2,5",[624,3511,3512],{"encoding":626},"g(x) = \\arcsin(2x) \\;\\Rightarrow\\; g'(x) = \\frac{2}{\\sqrt{1 - 4x^2}}, \\qquad g'(0{,}3) = \\frac{2}{\\sqrt{0{,}64}} = 2{,}5",[574,3514,3516,3543,3579,3635,3856,3987],{"className":3515,"ariaHidden":595},[631],[574,3517,3519,3522,3525,3528,3531,3534,3537,3540],{"className":3518},[635],[574,3520],{"className":3521,"style":873},[639],[574,3523,3412],{"className":3524,"style":732},[659,731],[574,3526,1108],{"className":3527},[648],[574,3529,917],{"className":3530},[659,731],[574,3532,1114],{"className":3533},[750],[574,3535],{"className":3536,"style":944},[758],[574,3538,998],{"className":3539},[948],[574,3541],{"className":3542,"style":944},[758],[574,3544,3546,3549,3552,3555,3558,3561,3564,3567,3570,3573,3576],{"className":3545},[635],[574,3547],{"className":3548,"style":873},[639],[574,3550,1217],{"className":3551},[1256],[574,3553,1108],{"className":3554},[648],[574,3556,610],{"className":3557},[659],[574,3559,917],{"className":3560},[659,731],[574,3562,1114],{"className":3563},[750],[574,3565],{"className":3566,"style":944},[758],[574,3568],{"className":3569,"style":944},[758],[574,3571,3439],{"className":3572},[948],[574,3574],{"className":3575,"style":944},[758],[574,3577],{"className":3578,"style":944},[758],[574,3580,3582,3585,3617,3620,3623,3626,3629,3632],{"className":3581},[635],[574,3583],{"className":3584,"style":1440},[639],[574,3586,3588,3591],{"className":3587},[659],[574,3589,3412],{"className":3590,"style":732},[659,731],[574,3592,3594],{"className":3593},[1142],[574,3595,3597],{"className":3596},[673],[574,3598,3600],{"className":3599},[678],[574,3601,3603],{"className":3602,"style":1471},[682],[574,3604,3605,3608],{"style":1474},[574,3606],{"className":3607,"style":1159},[690],[574,3609,3611],{"className":3610},[695,696,697,698],[574,3612,3614],{"className":3613},[659,698],[574,3615,1105],{"className":3616},[659,698],[574,3618,1108],{"className":3619},[648],[574,3621,917],{"className":3622},[659,731],[574,3624,1114],{"className":3625},[750],[574,3627],{"className":3628,"style":944},[758],[574,3630,998],{"className":3631},[948],[574,3633],{"className":3634,"style":944},[758],[574,3636,3638,3641,3788,3791,3794,3797,3829,3832,3835,3841,3844,3847,3850,3853],{"className":3637},[635],[574,3639],{"className":3640,"style":1502},[639],[574,3642,3644,3647,3785],{"className":3643},[659],[574,3645],{"className":3646},[648,666],[574,3648,3650],{"className":3649},[601],[574,3651,3653,3777],{"className":3652},[673,674],[574,3654,3656,3774],{"className":3655},[678],[574,3657,3659,3755,3763],{"className":3658,"style":1524},[682],[574,3660,3661,3664],{"style":1527},[574,3662],{"className":3663,"style":691},[690],[574,3665,3667],{"className":3666},[659],[574,3668,3670],{"className":3669},[659,1537],[574,3671,3673,3747],{"className":3672},[673,674],[574,3674,3676,3744],{"className":3675},[678],[574,3677,3679,3732],{"className":3678,"style":1547},[682],[574,3680,3682,3685],{"className":3681,"style":1552},[1551],[574,3683],{"className":3684,"style":691},[690],[574,3686,3688,3691,3694,3697,3700,3703],{"className":3687,"style":1559},[659],[574,3689,854],{"className":3690},[659],[574,3692],{"className":3693,"style":1266},[758],[574,3695,599],{"className":3696},[1270],[574,3698],{"className":3699,"style":1266},[758],[574,3701,3470],{"className":3702},[659],[574,3704,3706,3709],{"className":3705},[659],[574,3707,917],{"className":3708},[659,731],[574,3710,3712],{"className":3711},[1142],[574,3713,3715],{"className":3714},[673],[574,3716,3718],{"className":3717},[678],[574,3719,3721],{"className":3720,"style":1590},[682],[574,3722,3723,3726],{"style":1593},[574,3724],{"className":3725,"style":1159},[690],[574,3727,3729],{"className":3728},[695,696,697,698],[574,3730,610],{"className":3731},[659,698],[574,3733,3734,3737],{"style":1605},[574,3735],{"className":3736,"style":691},[690],[574,3738,3740],{"className":3739,"style":1613},[1612],[1615,3741,3742],{"xmlns":1617,"width":1618,"height":1619,"viewBox":1620,"preserveAspectRatio":1621},[1623,3743],{"d":1625},[574,3745,737],{"className":3746},[736],[574,3748,3750],{"className":3749},[678],[574,3751,3753],{"className":3752,"style":1635},[682],[574,3754],{},[574,3756,3757,3760],{"style":707},[574,3758],{"className":3759,"style":691},[690],[574,3761],{"className":3762,"style":715},[714],[574,3764,3765,3768],{"style":1648},[574,3766],{"className":3767,"style":691},[690],[574,3769,3771],{"className":3770},[659],[574,3772,610],{"className":3773},[659],[574,3775,737],{"className":3776},[736],[574,3778,3780],{"className":3779},[678],[574,3781,3783],{"className":3782,"style":1667},[682],[574,3784],{},[574,3786],{"className":3787},[750,666],[574,3789,613],{"className":3790},[754],[574,3792],{"className":3793,"style":3026},[758],[574,3795],{"className":3796,"style":759},[758],[574,3798,3800,3803],{"className":3799},[659],[574,3801,3412],{"className":3802,"style":732},[659,731],[574,3804,3806],{"className":3805},[1142],[574,3807,3809],{"className":3808},[673],[574,3810,3812],{"className":3811},[678],[574,3813,3815],{"className":3814,"style":1471},[682],[574,3816,3817,3820],{"style":1474},[574,3818],{"className":3819,"style":1159},[690],[574,3821,3823],{"className":3822},[695,696,697,698],[574,3824,3826],{"className":3825},[659,698],[574,3827,1105],{"className":3828},[659,698],[574,3830,1108],{"className":3831},[648],[574,3833,1111],{"className":3834},[659],[574,3836,3838],{"className":3837},[659],[574,3839,613],{"className":3840},[754],[574,3842,2817],{"className":3843},[659],[574,3845,1114],{"className":3846},[750],[574,3848],{"className":3849,"style":944},[758],[574,3851,998],{"className":3852},[948],[574,3854],{"className":3855,"style":944},[758],[574,3857,3859,3862,3978,3981,3984],{"className":3858},[635],[574,3860],{"className":3861,"style":1502},[639],[574,3863,3865,3868,3975],{"className":3864},[659],[574,3866],{"className":3867},[648,666],[574,3869,3871],{"className":3870},[601],[574,3872,3874,3967],{"className":3873},[673,674],[574,3875,3877,3964],{"className":3876},[678],[574,3878,3880,3945,3953],{"className":3879,"style":1524},[682],[574,3881,3882,3885],{"style":3115},[574,3883],{"className":3884,"style":691},[690],[574,3886,3888],{"className":3887},[659],[574,3889,3891],{"className":3890},[659,1537],[574,3892,3894,3937],{"className":3893},[673,674],[574,3895,3897,3934],{"className":3896},[678],[574,3898,3900,3922],{"className":3899,"style":3134},[682],[574,3901,3903,3906],{"className":3902,"style":1552},[1551],[574,3904],{"className":3905,"style":691},[690],[574,3907,3909,3912,3918],{"className":3908,"style":1559},[659],[574,3910,1111],{"className":3911},[659],[574,3913,3915],{"className":3914},[659],[574,3916,613],{"className":3917},[754],[574,3919,3921],{"className":3920},[659],"64",[574,3923,3924,3927],{"style":3159},[574,3925],{"className":3926,"style":691},[690],[574,3928,3930],{"className":3929,"style":1613},[1612],[1615,3931,3932],{"xmlns":1617,"width":1618,"height":1619,"viewBox":1620,"preserveAspectRatio":1621},[1623,3933],{"d":1625},[574,3935,737],{"className":3936},[736],[574,3938,3940],{"className":3939},[678],[574,3941,3943],{"className":3942,"style":3179},[682],[574,3944],{},[574,3946,3947,3950],{"style":707},[574,3948],{"className":3949,"style":691},[690],[574,3951],{"className":3952,"style":715},[714],[574,3954,3955,3958],{"style":1648},[574,3956],{"className":3957,"style":691},[690],[574,3959,3961],{"className":3960},[659],[574,3962,610],{"className":3963},[659],[574,3965,737],{"className":3966},[736],[574,3968,3970],{"className":3969},[678],[574,3971,3973],{"className":3972,"style":1667},[682],[574,3974],{},[574,3976],{"className":3977},[750,666],[574,3979],{"className":3980,"style":944},[758],[574,3982,998],{"className":3983},[948],[574,3985],{"className":3986,"style":944},[758],[574,3988,3990,3993,3996,4002],{"className":3989},[635],[574,3991],{"className":3992,"style":2724},[639],[574,3994,610],{"className":3995},[659],[574,3997,3999],{"className":3998},[659],[574,4000,613],{"className":4001},[754],[574,4003,2737],{"className":4004},[659],[565,4006,4007,4008,4073,4074,1080],{},"Hier muss ",[574,4009,4011,4036],{"className":4010},[577],[574,4012,4014],{"className":4013},[581],[583,4015,4016],{"xmlns":585},[587,4017,4018,4033],{},[590,4019,4020,4023,4025,4027,4029,4031],{},[604,4021,4022],{"mathvariant":1059},"∣",[608,4024,610],{},[604,4026,917],{},[604,4028,4022],{"mathvariant":1059},[593,4030,914],{},[608,4032,854],{},[624,4034,4035],{"encoding":626},"|2x| \u003C 1",[574,4037,4039,4064],{"className":4038,"ariaHidden":595},[631],[574,4040,4042,4045,4049,4052,4055,4058,4061],{"className":4041},[635],[574,4043],{"className":4044,"style":873},[639],[574,4046,4048],{"className":4047},[659],"∣2",[574,4050,917],{"className":4051},[659,731],[574,4053,4022],{"className":4054},[659],[574,4056],{"className":4057,"style":944},[758],[574,4059,914],{"className":4060},[948],[574,4062],{"className":4063,"style":944},[758],[574,4065,4067,4070],{"className":4066},[635],[574,4068],{"className":4069,"style":977},[639],[574,4071,854],{"className":4072},[659]," gelten, also ",[574,4075,4077,4103],{"className":4076},[577],[574,4078,4080],{"className":4079},[581],[583,4081,4082],{"xmlns":585},[587,4083,4084,4100],{},[590,4085,4086,4088,4090,4092,4094],{},[604,4087,4022],{"mathvariant":1059},[604,4089,917],{},[604,4091,4022],{"mathvariant":1059},[593,4093,914],{},[601,4095,4096,4098],{},[608,4097,854],{},[608,4099,610],{},[624,4101,4102],{"encoding":626},"|x| \u003C \\frac{1}{2}",[574,4104,4106,4130],{"className":4105,"ariaHidden":595},[631],[574,4107,4109,4112,4115,4118,4121,4124,4127],{"className":4108},[635],[574,4110],{"className":4111,"style":873},[639],[574,4113,4022],{"className":4114},[659],[574,4116,917],{"className":4117},[659,731],[574,4119,4022],{"className":4120},[659],[574,4122],{"className":4123,"style":944},[758],[574,4125,914],{"className":4126},[948],[574,4128],{"className":4129,"style":944},[758],[574,4131,4133,4137],{"className":4132},[635],[574,4134],{"className":4135,"style":4136},[639],"height:1.1901em;vertical-align:-0.345em;",[574,4138,4140,4143,4203],{"className":4139},[659],[574,4141],{"className":4142},[648,666],[574,4144,4146],{"className":4145},[601],[574,4147,4149,4195],{"className":4148},[673,674],[574,4150,4152,4192],{"className":4151},[678],[574,4153,4156,4170,4178],{"className":4154,"style":4155},[682],"height:0.8451em;",[574,4157,4158,4161],{"style":686},[574,4159],{"className":4160,"style":691},[690],[574,4162,4164],{"className":4163},[695,696,697,698],[574,4165,4167],{"className":4166},[659,698],[574,4168,610],{"className":4169},[659,698],[574,4171,4172,4175],{"style":707},[574,4173],{"className":4174,"style":691},[690],[574,4176],{"className":4177,"style":715},[714],[574,4179,4180,4183],{"style":718},[574,4181],{"className":4182,"style":691},[690],[574,4184,4186],{"className":4185},[695,696,697,698],[574,4187,4189],{"className":4188},[659,698],[574,4190,854],{"className":4191},[659,698],[574,4193,737],{"className":4194},[736],[574,4196,4198],{"className":4197},[678],[574,4199,4201],{"className":4200,"style":744},[682],[574,4202],{},[574,4204],{"className":4205},[750,666],[560,4207,4209],{"id":4208},"typische-fehler","Typische Fehler",[4211,4212,4213,4545,4548,4911],"ul",{},[4214,4215,4216,4298,4299,4422,4423,4544],"li",{},[574,4217,4219,4245],{"className":4218},[577],[574,4220,4222],{"className":4221},[581],[583,4223,4224],{"xmlns":585},[587,4225,4226,4242],{},[590,4227,4228,4230,4232,4234,4236],{},[593,4229,1108],{"stretchy":849},[604,4231,1217],{},[593,4233,1220],{},[604,4235,917],{},[1097,4237,4238,4240],{},[593,4239,1114],{"stretchy":849},[593,4241,1105],{"mathvariant":1059,"lspace":1104,"rspace":1104},[624,4243,4244],{"encoding":626},"(\\arcsin x)'",[574,4246,4248],{"className":4247,"ariaHidden":595},[631],[574,4249,4251,4254,4257,4260,4263,4266],{"className":4250},[635],[574,4252],{"className":4253,"style":1131},[639],[574,4255,1108],{"className":4256},[648],[574,4258,1217],{"className":4259},[1256],[574,4261],{"className":4262,"style":759},[758],[574,4264,917],{"className":4265},[659,731],[574,4267,4269,4272],{"className":4268},[750],[574,4270,1114],{"className":4271},[750],[574,4273,4275],{"className":4274},[1142],[574,4276,4278],{"className":4277},[673],[574,4279,4281],{"className":4280},[678],[574,4282,4284],{"className":4283,"style":1152},[682],[574,4285,4286,4289],{"style":1155},[574,4287],{"className":4288,"style":1159},[690],[574,4290,4292],{"className":4291},[695,696,697,698],[574,4293,4295],{"className":4294},[659,698],[574,4296,1105],{"className":4297},[659,698]," mit ",[574,4300,4302,4326],{"className":4301},[577],[574,4303,4305],{"className":4304},[581],[583,4306,4307],{"xmlns":585},[587,4308,4309,4323],{},[590,4310,4311],{},[601,4312,4313,4315],{},[608,4314,854],{},[590,4316,4317,4319,4321],{},[604,4318,1759],{},[593,4320,1220],{},[604,4322,917],{},[624,4324,4325],{"encoding":626},"\\frac{1}{\\sin x}",[574,4327,4329],{"className":4328,"ariaHidden":595},[631],[574,4330,4332,4335],{"className":4331},[635],[574,4333],{"className":4334,"style":4136},[639],[574,4336,4338,4341,4419],{"className":4337},[659],[574,4339],{"className":4340},[648,666],[574,4342,4344],{"className":4343},[601],[574,4345,4347,4411],{"className":4346},[673,674],[574,4348,4350,4408],{"className":4349},[678],[574,4351,4353,4386,4394],{"className":4352,"style":4155},[682],[574,4354,4355,4358],{"style":686},[574,4356],{"className":4357,"style":691},[690],[574,4359,4361],{"className":4360},[695,696,697,698],[574,4362,4364,4379,4383],{"className":4363},[659,698],[574,4365,4367,4371,4375],{"className":4366},[1256,698],[574,4368,4370],{"className":4369},[698],"s",[574,4372,4374],{"className":4373},[698],"i",[574,4376,4378],{"className":4377},[698],"n",[574,4380],{"className":4381,"style":4382},[758,698],"margin-right:0.1952em;",[574,4384,917],{"className":4385},[659,731,698],[574,4387,4388,4391],{"style":707},[574,4389],{"className":4390,"style":691},[690],[574,4392],{"className":4393,"style":715},[714],[574,4395,4396,4399],{"style":718},[574,4397],{"className":4398,"style":691},[690],[574,4400,4402],{"className":4401},[695,696,697,698],[574,4403,4405],{"className":4404},[659,698],[574,4406,854],{"className":4407},[659,698],[574,4409,737],{"className":4410},[736],[574,4412,4414],{"className":4413},[678],[574,4415,4417],{"className":4416,"style":744},[682],[574,4418],{},[574,4420],{"className":4421},[750,666]," oder ",[574,4424,4426,4450],{"className":4425},[577],[574,4427,4429],{"className":4428},[581],[583,4430,4431],{"xmlns":585},[587,4432,4433,4447],{},[590,4434,4435],{},[601,4436,4437,4439],{},[608,4438,854],{},[590,4440,4441,4443,4445],{},[604,4442,1847],{},[593,4444,1220],{},[604,4446,917],{},[624,4448,4449],{"encoding":626},"\\frac{1}{\\cos x}",[574,4451,4453],{"className":4452,"ariaHidden":595},[631],[574,4454,4456,4459],{"className":4455},[635],[574,4457],{"className":4458,"style":4136},[639],[574,4460,4462,4465,4541],{"className":4461},[659],[574,4463],{"className":4464},[648,666],[574,4466,4468],{"className":4467},[601],[574,4469,4471,4533],{"className":4470},[673,674],[574,4472,4474,4530],{"className":4473},[678],[574,4475,4477,4508,4516],{"className":4476,"style":4155},[682],[574,4478,4479,4482],{"style":686},[574,4480],{"className":4481,"style":691},[690],[574,4483,4485],{"className":4484},[695,696,697,698],[574,4486,4488,4502,4505],{"className":4487},[659,698],[574,4489,4491,4495,4499],{"className":4490},[1256,698],[574,4492,4494],{"className":4493},[698],"c",[574,4496,4498],{"className":4497},[698],"o",[574,4500,4370],{"className":4501},[698],[574,4503],{"className":4504,"style":4382},[758,698],[574,4506,917],{"className":4507},[659,731,698],[574,4509,4510,4513],{"style":707},[574,4511],{"className":4512,"style":691},[690],[574,4514],{"className":4515,"style":715},[714],[574,4517,4518,4521],{"style":718},[574,4519],{"className":4520,"style":691},[690],[574,4522,4524],{"className":4523},[695,696,697,698],[574,4525,4527],{"className":4526},[659,698],[574,4528,854],{"className":4529},[659,698],[574,4531,737],{"className":4532},[736],[574,4534,4536],{"className":4535},[678],[574,4537,4539],{"className":4538,"style":744},[682],[574,4540],{},[574,4542],{"className":4543},[750,666]," verwechseln. Der Arkussinus ist die Umkehrfunktion, nicht der Kehrwert des Sinus.",[4214,4546,4547],{},"Das Minus beim Arkuskosinus vergessen. Der Arkuskosinus fällt, seine Ableitung ist negativ.",[4214,4549,4550,4551,4881,4882,4910],{},"Die innere Ableitung vergessen: ",[574,4552,4554,4609],{"className":4553},[577],[574,4555,4557],{"className":4556},[581],[583,4558,4559],{"xmlns":585},[587,4560,4561,4606],{},[590,4562,4563,4565,4567,4569,4571,4573,4575,4577,4583,4586],{},[593,4564,1108],{"stretchy":849},[604,4566,1217],{},[593,4568,1220],{},[593,4570,1108],{"stretchy":849},[608,4572,610],{},[604,4574,917],{},[593,4576,1114],{"stretchy":849},[1097,4578,4579,4581],{},[593,4580,1114],{"stretchy":849},[593,4582,1105],{"mathvariant":1059,"lspace":1104,"rspace":1104},[593,4584,4585],{"mathvariant":1059},"≠",[601,4587,4588,4590],{},[608,4589,854],{},[1414,4591,4592],{},[590,4593,4594,4596,4598,4600],{},[608,4595,854],{},[593,4597,599],{},[608,4599,3470],{},[1097,4601,4602,4604],{},[604,4603,917],{},[608,4605,610],{},[624,4607,4608],{"encoding":626},"(\\arcsin(2x))' \\neq \\frac{1}{\\sqrt{1 - 4x^2}}",[574,4610,4612,4718],{"className":4611,"ariaHidden":595},[631],[574,4613,4615,4618,4621,4624,4627,4630,4633,4636,4668,4671,4715],{"className":4614},[635],[574,4616],{"className":4617,"style":1131},[639],[574,4619,1108],{"className":4620},[648],[574,4622,1217],{"className":4623},[1256],[574,4625,1108],{"className":4626},[648],[574,4628,610],{"className":4629},[659],[574,4631,917],{"className":4632},[659,731],[574,4634,1114],{"className":4635},[750],[574,4637,4639,4642],{"className":4638},[750],[574,4640,1114],{"className":4641},[750],[574,4643,4645],{"className":4644},[1142],[574,4646,4648],{"className":4647},[673],[574,4649,4651],{"className":4650},[678],[574,4652,4654],{"className":4653,"style":1152},[682],[574,4655,4656,4659],{"style":1155},[574,4657],{"className":4658,"style":1159},[690],[574,4660,4662],{"className":4661},[695,696,697,698],[574,4663,4665],{"className":4664},[659,698],[574,4666,1105],{"className":4667},[659,698],[574,4669],{"className":4670,"style":944},[758],[574,4672,4674,4708,4712],{"className":4673},[948],[574,4675,4677],{"className":4676},[948],[574,4678,4681],{"className":4679},[659,4680],"vbox",[574,4682,4685],{"className":4683},[4684],"thinbox",[574,4686,4689,4693,4704],{"className":4687},[4688],"rlap",[574,4690],{"className":4691,"style":4692},[639],"height:0.8889em;vertical-align:-0.1944em;",[574,4694,4697],{"className":4695},[4696],"inner",[574,4698,4700],{"className":4699},[659],[574,4701,4703],{"className":4702},[948],"",[574,4705],{"className":4706},[4707],"fix",[574,4709],{"className":4710},[758,4711],"nobreak",[574,4713,998],{"className":4714},[948],[574,4716],{"className":4717,"style":944},[758],[574,4719,4721,4725],{"className":4720},[635],[574,4722],{"className":4723,"style":4724},[639],"height:1.3831em;vertical-align:-0.538em;",[574,4726,4728,4731,4878],{"className":4727},[659],[574,4729],{"className":4730},[648,666],[574,4732,4734],{"className":4733},[601],[574,4735,4737,4869],{"className":4736},[673,674],[574,4738,4740,4866],{"className":4739},[678],[574,4741,4743,4844,4852],{"className":4742,"style":4155},[682],[574,4744,4746,4749],{"style":4745},"top:-2.5445em;",[574,4747],{"className":4748,"style":691},[690],[574,4750,4752],{"className":4751},[695,696,697,698],[574,4753,4755],{"className":4754},[659,698],[574,4756,4758],{"className":4757},[659,1537,698],[574,4759,4761,4835],{"className":4760},[673,674],[574,4762,4764,4832],{"className":4763},[678],[574,4765,4768,4819],{"className":4766,"style":4767},[682],"height:0.9221em;",[574,4769,4771,4774],{"className":4770,"style":1552},[1551],[574,4772],{"className":4773,"style":691},[690],[574,4775,4777,4780,4783,4786],{"className":4776,"style":1559},[659,698],[574,4778,854],{"className":4779},[659,698],[574,4781,599],{"className":4782},[1270,698],[574,4784,3470],{"className":4785},[659,698],[574,4787,4789,4792],{"className":4788},[659,698],[574,4790,917],{"className":4791},[659,731,698],[574,4793,4795],{"className":4794},[1142],[574,4796,4798],{"className":4797},[673],[574,4799,4801],{"className":4800},[678],[574,4802,4805],{"className":4803,"style":4804},[682],"height:0.7463em;",[574,4806,4808,4812],{"style":4807},"top:-2.786em;margin-right:0.0714em;",[574,4809],{"className":4810,"style":4811},[690],"height:2.5em;",[574,4813,4816],{"className":4814},[695,4815,655,698],"reset-size3",[574,4817,610],{"className":4818},[659,698],[574,4820,4822,4825],{"style":4821},"top:-2.8821em;",[574,4823],{"className":4824,"style":691},[690],[574,4826,4828],{"className":4827,"style":1613},[1612,698],[1615,4829,4830],{"xmlns":1617,"width":1618,"height":1619,"viewBox":1620,"preserveAspectRatio":1621},[1623,4831],{"d":1625},[574,4833,737],{"className":4834},[736],[574,4836,4838],{"className":4837},[678],[574,4839,4842],{"className":4840,"style":4841},[682],"height:0.1179em;",[574,4843],{},[574,4845,4846,4849],{"style":707},[574,4847],{"className":4848,"style":691},[690],[574,4850],{"className":4851,"style":715},[714],[574,4853,4854,4857],{"style":718},[574,4855],{"className":4856,"style":691},[690],[574,4858,4860],{"className":4859},[695,696,697,698],[574,4861,4863],{"className":4862},[659,698],[574,4864,854],{"className":4865},[659,698],[574,4867,737],{"className":4868},[736],[574,4870,4872],{"className":4871},[678],[574,4873,4876],{"className":4874,"style":4875},[682],"height:0.538em;",[574,4877],{},[574,4879],{"className":4880},[750,666],", der Faktor ",[574,4883,4885,4898],{"className":4884},[577],[574,4886,4888],{"className":4887},[581],[583,4889,4890],{"xmlns":585},[587,4891,4892,4896],{},[590,4893,4894],{},[608,4895,610],{},[624,4897,610],{"encoding":626},[574,4899,4901],{"className":4900,"ariaHidden":595},[631],[574,4902,4904,4907],{"className":4903},[635],[574,4905],{"className":4906,"style":977},[639],[574,4908,610],{"className":4909},[659]," fehlt.",[4214,4912,4913,4914,4969],{},"Die Ableitung bei ",[574,4915,4917,4936],{"className":4916},[577],[574,4918,4920],{"className":4919},[581],[583,4921,4922],{"xmlns":585},[587,4923,4924,4934],{},[590,4925,4926,4928,4930,4932],{},[604,4927,917],{},[593,4929,998],{},[593,4931,1001],{},[608,4933,854],{},[624,4935,1006],{"encoding":626},[574,4937,4939,4957],{"className":4938,"ariaHidden":595},[631],[574,4940,4942,4945,4948,4951,4954],{"className":4941},[635],[574,4943],{"className":4944,"style":1016},[639],[574,4946,917],{"className":4947},[659,731],[574,4949],{"className":4950,"style":944},[758],[574,4952,998],{"className":4953},[948],[574,4955],{"className":4956,"style":944},[758],[574,4958,4960,4963,4966],{"className":4959},[635],[574,4961],{"className":4962,"style":934},[639],[574,4964,1001],{"className":4965},[659],[574,4967,854],{"className":4968},[659]," auswerten. Dort ist der Nenner null, die Ableitung existiert nicht.",{"title":4971,"searchDepth":4972,"depth":4972,"links":4973},"",2,[4974,4975,4976,4977],{"id":562,"depth":4972,"text":563},{"id":1675,"depth":4972,"text":1676},{"id":2619,"depth":4972,"text":2620},{"id":4208,"depth":4972,"text":4209},[4979,4983,4986,4991,4994,4996,4999,5002,5005,5008,5012],{"lhs":4980,"rhs":1111,"where":4981},"round((asin(x+1e-5) - asin(x-1e-5))\u002F(2e-5) - 1\u002Fsqrt(1 - x^2), 6)",{"x":4982},0.3,{"lhs":4980,"rhs":1111,"where":4984},{"x":4985},-0.7,{"lhs":4987,"rhs":4988,"where":4989},"cos(asin(x))","sqrt(1 - x^2)",{"x":4990},0.6,{"lhs":4987,"rhs":4988,"where":4992},{"x":4993},-0.4,{"lhs":4995,"rhs":854},"1\u002Fsqrt(1 - 0^2)",{"lhs":4997,"rhs":4998},"1\u002Fsqrt(1 - 0.5^2)","2\u002Fsqrt(3)",{"lhs":5000,"rhs":5001},"round(2\u002Fsqrt(3), 4)","1.1547",{"lhs":5003,"rhs":1111,"where":5004},"round((asin(2*(x+1e-5)) - asin(2*(x-1e-5)))\u002F(2e-5) - 2\u002Fsqrt(1 - 4*x^2), 6)",{"x":4982},{"lhs":5006,"rhs":5007},"2\u002Fsqrt(1 - 4*0.3^2)","2.5",{"lhs":5009,"rhs":1111,"where":5010},"round((acos(x+1e-5) - acos(x-1e-5))\u002F(2e-5) + 1\u002Fsqrt(1 - x^2), 6)",{"x":5011},0.2,{"lhs":5013,"rhs":5014,"where":5015},"asin(x) + acos(x)","pi\u002F2",{"x":5016},0.35,"\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo><\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">-1 < x < 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:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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","derivative-arcsin","f(x) = \\arcsin x \\;\\Rightarrow\\; f'(x) = \\frac{1}{\\sqrt{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>arcsin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmsqrt>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x) = \\arcsin x \\;\\Rightarrow\\; f'(x) = \\frac{1}{\\sqrt{1 - x^2}}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6679em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">arcsin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0519em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.2514em;vertical-align:-0.93em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.1966em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9134em;\">\u003Cspan class=\"svg-align\" style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:0.833em;\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7401em;\">\u003Cspan style=\"top:-2.989em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.8734em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\">\u003Csvg 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