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x",[568,986,988,1052,1214,1293,1440],{"className":987,"ariaHidden":605},[604],[568,989,991,995,998,1002,1006,1009,1043,1046,1049],{"className":990},[609],[568,992],{"className":993,"style":994},[613],"height:1.0519em;vertical-align:-0.25em;",[568,996,674],{"className":997},[727],[568,999,877],{"className":1000},[1001],"mop",[568,1003],{"className":1004,"style":1005},[801],"margin-right:0.1667em;",[568,1007,595],{"className":1008},[618,622],[568,1010,1012,1015],{"className":1011},[767],[568,1013,690],{"className":1014},[767],[568,1016,1018],{"className":1017},[626],[568,1019,1021],{"className":1020},[630],[568,1022,1024],{"className":1023},[634],[568,1025,1028],{"className":1026,"style":1027},[638],"height:0.8019em;",[568,1029,1031,1034],{"style":1030},"top:-3.113em;margin-right:0.05em;",[568,1032],{"className":1033,"style":646},[645],[568,1035,1037],{"className":1036},[650,651,652,653],[568,1038,1040],{"className":1039},[618,653],[568,1041,695],{"className":1042},[618,653],[568,1044],{"className":1045,"style":802},[801],[568,1047,698],{"className":1048},[806],[568,1050],{"className":1051,"style":802},[801],[568,1053,1055,1059,1205,1208,1211],{"className":1054},[609],[568,1056],{"className":1057,"style":1058},[613],"height:2.1343em;vertical-align:-0.686em;",[568,1060,1062,1066,1202],{"className":1061},[618],[568,1063],{"className":1064},[727,1065],"nulldelimiter",[568,1067,1069],{"className":1068},[892],[568,1070,1073,1193],{"className":1071},[630,1072],"vlist-t2",[568,1074,1076,1188],{"className":1075},[634],[568,1077,1080,1093,1104],{"className":1078,"style":1079},[638],"height:1.4483em;",[568,1081,1083,1087],{"style":1082},"top:-2.314em;",[568,1084],{"className":1085,"style":1086},[645],"height:3em;",[568,1088,1090],{"className":1089},[618],[568,1091,918],{"className":1092},[618],[568,1094,1096,1099],{"style":1095},"top:-3.23em;",[568,1097],{"className":1098,"style":1086},[645],[568,1100],{"className":1101,"style":1103},[1102],"frac-line","border-bottom-width:0.04em;",[568,1105,1107,1110],{"style":1106},"top:-3.677em;",[568,1108],{"className":1109,"style":1086},[645],[568,1111,1113,1142,1146,1150,1153],{"className":1112},[618],[568,1114,1116,1119],{"className":1115},[618],[568,1117,592],{"className":1118},[618,622],[568,1120,1122],{"className":1121},[626],[568,1123,1125],{"className":1124},[630],[568,1126,1128],{"className":1127},[634],[568,1129,1131],{"className":1130,"style":614},[638],[568,1132,1133,1136],{"style":641},[568,1134],{"className":1135,"style":646},[645],[568,1137,1139],{"className":1138},[650,651,652,653],[568,1140,595],{"className":1141},[618,622,653],[568,1143],{"className":1144,"style":1145},[801],"margin-right:0.2222em;",[568,1147,904],{"className":1148},[1149],"mbin",[568,1151],{"className":1152,"style":1145},[801],[568,1154,1156,1159],{"className":1155},[618],[568,1157,592],{"className":1158},[618,622],[568,1160,1162],{"className":1161},[626],[568,1163,1165],{"className":1164},[630],[568,1166,1168],{"className":1167},[634],[568,1169,1171],{"className":1170,"style":746},[638],[568,1172,1173,1176],{"style":641},[568,1174],{"className":1175,"style":646},[645],[568,1177,1179],{"className":1178},[650,651,652,653],[568,1180,1182,1185],{"className":1181},[618,653],[568,1183,683],{"className":1184},[618,653],[568,1186,595],{"className":1187},[618,622,653],[568,1189,1192],{"className":1190},[1191],"vlist-s","​",[568,1194,1196],{"className":1195},[634],[568,1197,1200],{"className":1198,"style":1199},[638],"height:0.686em;",[568,1201],{},[568,1203],{"className":1204},[767,1065],[568,1206],{"className":1207,"style":802},[801],[568,1209,698],{"className":1210},[806],[568,1212],{"className":1213,"style":802},[801],[568,1215,1217,1220,1223,1226,1229,1233,1237,1240,1243,1246,1249,1252,1284,1287,1290],{"className":1216},[609],[568,1218],{"className":1219,"style":994},[613],[568,1221,923],{"className":1222},[1001],[568,1224],{"className":1225,"style":1005},[801],[568,1227,595],{"className":1228},[618,622],[568,1230,930],{"className":1231},[1232],"mpunct",[568,1234],{"className":1235,"style":1236},[801],"margin-right:2em;",[568,1238],{"className":1239,"style":1005},[801],[568,1241,674],{"className":1242},[727],[568,1244,923],{"className":1245},[1001],[568,1247],{"className":1248,"style":1005},[801],[568,1250,595],{"className":1251},[618,622],[568,1253,1255,1258],{"className":1254},[767],[568,1256,690],{"className":1257},[767],[568,1259,1261],{"className":1260},[626],[568,1262,1264],{"className":1263},[630],[568,1265,1267],{"className":1266},[634],[568,1268,1270],{"className":1269,"style":1027},[638],[568,1271,1272,1275],{"style":1030},[568,1273],{"className":1274,"style":646},[645],[568,1276,1278],{"className":1277},[650,651,652,653],[568,1279,1281],{"className":1280},[618,653],[568,1282,695],{"className":1283},[618,653],[568,1285],{"className":1286,"style":802},[801],[568,1288,698],{"className":1289},[806],[568,1291],{"className":1292,"style":802},[801],[568,1294,1296,1299,1431,1434,1437],{"className":1295},[609],[568,1297],{"className":1298,"style":1058},[613],[568,1300,1302,1305,1428],{"className":1301},[618],[568,1303],{"className":1304},[727,1065],[568,1306,1308],{"className":1307},[892],[568,1309,1311,1420],{"className":1310},[630,1072],[568,1312,1314,1417],{"className":1313},[634],[568,1315,1317,1328,1336],{"className":1316,"style":1079},[638],[568,1318,1319,1322],{"style":1082},[568,1320],{"className":1321,"style":1086},[645],[568,1323,1325],{"className":1324},[618],[568,1326,918],{"className":1327},[618],[568,1329,1330,1333],{"style":1095},[568,1331],{"className":1332,"style":1086},[645],[568,1334],{"className":1335,"style":1103},[1102],[568,1337,1338,1341],{"style":1106},[568,1339],{"className":1340,"style":1086},[645],[568,1342,1344,1373,1376,1379,1382],{"className":1343},[618],[568,1345,1347,1350],{"className":1346},[618],[568,1348,592],{"className":1349},[618,622],[568,1351,1353],{"className":1352},[626],[568,1354,1356],{"className":1355},[630],[568,1357,1359],{"className":1358},[634],[568,1360,1362],{"className":1361,"style":614},[638],[568,1363,1364,1367],{"style":641},[568,1365],{"className":1366,"style":646},[645],[568,1368,1370],{"className":1369},[650,651,652,653],[568,1371,595],{"className":1372},[618,622,653],[568,1374],{"className":1375,"style":1145},[801],[568,1377,683],{"className":1378},[1149],[568,1380],{"className":1381,"style":1145},[801],[568,1383,1385,1388],{"className":1384},[618],[568,1386,592],{"className":1387},[618,622],[568,1389,1391],{"className":1390},[626],[568,1392,1394],{"className":1393},[630],[568,1395,1397],{"className":1396},[634],[568,1398,1400],{"className":1399,"style":746},[638],[568,1401,1402,1405],{"style":641},[568,1403],{"className":1404,"style":646},[645],[568,1406,1408],{"className":1407},[650,651,652,653],[568,1409,1411,1414],{"className":1410},[618,653],[568,1412,683],{"className":1413},[618,653],[568,1415,595],{"className":1416},[618,622,653],[568,1418,1192],{"className":1419},[1191],[568,1421,1423],{"className":1422},[634],[568,1424,1426],{"className":1425,"style":1199},[638],[568,1427],{},[568,1429],{"className":1430},[767,1065],[568,1432],{"className":1433,"style":802},[801],[568,1435,698],{"className":1436},[806],[568,1438],{"className":1439,"style":802},[801],[568,1441,1443,1447,1450,1453],{"className":1442},[609],[568,1444],{"className":1445,"style":1446},[613],"height:0.6944em;",[568,1448,877],{"className":1449},[1001],[568,1451],{"className":1452,"style":1005},[801],[568,1454,595],{"className":1455},[618,622],[564,1457,1458,1459,1492,1493,1526,1527,1531,1532,1624,1625,1665,1666,1761],{},"Anders als bei ",[568,1460,1462,1479],{"className":1461},[571],[568,1463,1465],{"className":1464},[575],[577,1466,1467],{"xmlns":579},[581,1468,1469,1476],{},[584,1470,1471,1474],{},[590,1472,1473],{},"sin",[671,1475,880],{},[597,1477,1478],{"encoding":599},"\\sin",[568,1480,1482],{"className":1481,"ariaHidden":605},[604],[568,1483,1485,1489],{"className":1484},[609],[568,1486],{"className":1487,"style":1488},[613],"height:0.6679em;",[568,1490,1473],{"className":1491},[1001]," und ",[568,1494,1496,1513],{"className":1495},[571],[568,1497,1499],{"className":1498},[575],[577,1500,1501],{"xmlns":579},[581,1502,1503,1510],{},[584,1504,1505,1508],{},[590,1506,1507],{},"cos",[671,1509,880],{},[597,1511,1512],{"encoding":599},"\\cos",[568,1514,1516],{"className":1515,"ariaHidden":605},[604],[568,1517,1519,1523],{"className":1518},[609],[568,1520],{"className":1521,"style":1522},[613],"height:0.4306em;",[568,1524,1507],{"className":1525},[1001]," gibt es ",[1528,1529,1530],"strong",{},"kein Minuszeichen",": ",[568,1533,1535,1563],{"className":1534},[571],[568,1536,1538],{"className":1537},[575],[577,1539,1540],{"xmlns":579},[581,1541,1542,1560],{},[584,1543,1544,1554,1556,1558],{},[587,1545,1546,1552],{},[584,1547,1548,1550],{},[590,1549,923],{},[671,1551,880],{},[671,1553,695],{"mathvariant":693,"lspace":694,"rspace":694},[671,1555,698],{},[590,1557,877],{},[671,1559,880],{},[597,1561,1562],{"encoding":599},"\\cosh' = \\sinh",[568,1564,1566,1615],{"className":1565,"ariaHidden":605},[604],[568,1567,1569,1573,1606,1609,1612],{"className":1568},[609],[568,1570],{"className":1571,"style":1572},[613],"height:0.8362em;",[568,1574,1576,1579],{"className":1575},[1001],[568,1577,923],{"className":1578},[1001],[568,1580,1582],{"className":1581},[626],[568,1583,1585],{"className":1584},[630],[568,1586,1588],{"className":1587},[634],[568,1589,1591],{"className":1590,"style":1572},[638],[568,1592,1594,1597],{"style":1593},"top:-3.1473em;margin-right:0.05em;",[568,1595],{"className":1596,"style":646},[645],[568,1598,1600],{"className":1599},[650,651,652,653],[568,1601,1603],{"className":1602},[618,653],[568,1604,695],{"className":1605},[618,653],[568,1607],{"className":1608,"style":802},[801],[568,1610,698],{"className":1611},[806],[568,1613],{"className":1614,"style":802},[801],[568,1616,1618,1621],{"className":1617},[609],[568,1619],{"className":1620,"style":1446},[613],[568,1622,877],{"className":1623},[1001],", nicht ",[568,1626,1628,1646],{"className":1627},[571],[568,1629,1631],{"className":1630},[575],[577,1632,1633],{"xmlns":579},[581,1634,1635,1643],{},[584,1636,1637,1639,1641],{},[671,1638,683],{},[590,1640,877],{},[671,1642,880],{},[597,1644,1645],{"encoding":599},"-\\sinh",[568,1647,1649],{"className":1648,"ariaHidden":605},[604],[568,1650,1652,1656,1659,1662],{"className":1651},[609],[568,1653],{"className":1654,"style":1655},[613],"height:0.7778em;vertical-align:-0.0833em;",[568,1657,683],{"className":1658},[618],[568,1660],{"className":1661,"style":1005},[801],[568,1663,877],{"className":1664},[1001],". Zweimal abgeleitet erhält man die Funktion selbst zurück, ",[568,1667,1669,1701],{"className":1668},[571],[568,1670,1672],{"className":1671},[575],[577,1673,1674],{"xmlns":579},[581,1675,1676,1698],{},[584,1677,1678,1692,1694,1696],{},[587,1679,1680,1686],{},[584,1681,1682,1684],{},[590,1683,877],{},[671,1685,880],{},[584,1687,1688,1690],{},[671,1689,695],{"mathvariant":693},[671,1691,695],{"mathvariant":693},[671,1693,698],{},[590,1695,877],{},[671,1697,880],{},[597,1699,1700],{"encoding":599},"\\sinh'' = \\sinh",[568,1702,1704,1752],{"className":1703,"ariaHidden":605},[604],[568,1705,1707,1710,1743,1746,1749],{"className":1706},[609],[568,1708],{"className":1709,"style":1572},[613],[568,1711,1713,1716],{"className":1712},[1001],[568,1714,877],{"className":1715},[1001],[568,1717,1719],{"className":1718},[626],[568,1720,1722],{"className":1721},[630],[568,1723,1725],{"className":1724},[634],[568,1726,1728],{"className":1727,"style":1572},[638],[568,1729,1730,1733],{"style":1593},[568,1731],{"className":1732,"style":646},[645],[568,1734,1736],{"className":1735},[650,651,652,653],[568,1737,1739],{"className":1738},[618,653],[568,1740,1742],{"className":1741},[618,653],"′′",[568,1744],{"className":1745,"style":802},[801],[568,1747,698],{"className":1748},[806],[568,1750],{"className":1751,"style":802},[801],[568,1753,1755,1758],{"className":1754},[609],[568,1756],{"className":1757,"style":1446},[613],[568,1759,877],{"className":1760},[1001],".",[564,1763,1764,1765,1797,1798,1959,1960,2152,2153,2183],{},"Die Ableitung von ",[568,1766,1768,1785],{"className":1767},[571],[568,1769,1771],{"className":1770},[575],[577,1772,1773],{"xmlns":579},[581,1774,1775,1782],{},[584,1776,1777,1780],{},[590,1778,1779],{},"tanh",[671,1781,880],{},[597,1783,1784],{"encoding":599},"\\tanh",[568,1786,1788],{"className":1787,"ariaHidden":605},[604],[568,1789,1791,1794],{"className":1790},[609],[568,1792],{"className":1793,"style":1446},[613],[568,1795,1779],{"className":1796},[1001]," folgt mit der Quotientenregel und ",[568,1799,1801,1844],{"className":1800},[571],[568,1802,1804],{"className":1803},[575],[577,1805,1806],{"xmlns":579},[581,1807,1808,1841],{},[584,1809,1810,1820,1822,1824,1834,1836,1838],{},[587,1811,1812,1818],{},[584,1813,1814,1816],{},[590,1815,923],{},[671,1817,880],{},[916,1819,918],{},[590,1821,595],{},[671,1823,683],{},[587,1825,1826,1832],{},[584,1827,1828,1830],{},[590,1829,877],{},[671,1831,880],{},[916,1833,918],{},[590,1835,595],{},[671,1837,698],{},[916,1839,1840],{},"1",[597,1842,1843],{"encoding":599},"\\cosh^2 x - \\sinh^2 x = 1",[568,1845,1847,1899,1949],{"className":1846,"ariaHidden":605},[604],[568,1848,1850,1854,1884,1887,1890,1893,1896],{"className":1849},[609],[568,1851],{"className":1852,"style":1853},[613],"height:0.9818em;vertical-align:-0.0833em;",[568,1855,1857,1860],{"className":1856},[1001],[568,1858,923],{"className":1859},[1001],[568,1861,1863],{"className":1862},[626],[568,1864,1866],{"className":1865},[630],[568,1867,1869],{"className":1868},[634],[568,1870,1873],{"className":1871,"style":1872},[638],"height:0.8984em;",[568,1874,1875,1878],{"style":1593},[568,1876],{"className":1877,"style":646},[645],[568,1879,1881],{"className":1880},[650,651,652,653],[568,1882,918],{"className":1883},[618,653],[568,1885],{"className":1886,"style":1005},[801],[568,1888,595],{"className":1889},[618,622],[568,1891],{"className":1892,"style":1145},[801],[568,1894,683],{"className":1895},[1149],[568,1897],{"className":1898,"style":1145},[801],[568,1900,1902,1905,1934,1937,1940,1943,1946],{"className":1901},[609],[568,1903],{"className":1904,"style":1872},[613],[568,1906,1908,1911],{"className":1907},[1001],[568,1909,877],{"className":1910},[1001],[568,1912,1914],{"className":1913},[626],[568,1915,1917],{"className":1916},[630],[568,1918,1920],{"className":1919},[634],[568,1921,1923],{"className":1922,"style":1872},[638],[568,1924,1925,1928],{"style":1593},[568,1926],{"className":1927,"style":646},[645],[568,1929,1931],{"className":1930},[650,651,652,653],[568,1932,918],{"className":1933},[618,653],[568,1935],{"className":1936,"style":1005},[801],[568,1938,595],{"className":1939},[618,622],[568,1941],{"className":1942,"style":802},[801],[568,1944,698],{"className":1945},[806],[568,1947],{"className":1948,"style":802},[801],[568,1950,1952,1956],{"className":1951},[609],[568,1953],{"className":1954,"style":1955},[613],"height:0.6444em;",[568,1957,1840],{"className":1958},[618],". Weil ",[568,1961,1963,1999],{"className":1962},[571],[568,1964,1966],{"className":1965},[575],[577,1967,1968],{"xmlns":579},[581,1969,1970,1996],{},[584,1971,1972,1990,1993],{},[892,1973,1974,1976],{},[916,1975,1840],{},[584,1977,1978,1988],{},[587,1979,1980,1986],{},[584,1981,1982,1984],{},[590,1983,923],{},[671,1985,880],{},[916,1987,918],{},[590,1989,595],{},[671,1991,1992],{},">",[916,1994,1995],{},"0",[597,1997,1998],{"encoding":599},"\\frac{1}{\\cosh^2 x} > 0",[568,2000,2002,2143],{"className":2001,"ariaHidden":605},[604],[568,2003,2005,2009,2134,2137,2140],{"className":2004},[609],[568,2006],{"className":2007,"style":2008},[613],"height:1.2164em;vertical-align:-0.3713em;",[568,2010,2012,2015,2131],{"className":2011},[618],[568,2013],{"className":2014},[727,1065],[568,2016,2018],{"className":2017},[892],[568,2019,2021,2122],{"className":2020},[630,1072],[568,2022,2024,2119],{"className":2023},[634],[568,2025,2028,2096,2104],{"className":2026,"style":2027},[638],"height:0.8451em;",[568,2029,2031,2034],{"style":2030},"top:-2.6287em;",[568,2032],{"className":2033,"style":1086},[645],[568,2035,2037],{"className":2036},[650,651,652,653],[568,2038,2040,2089,2093],{"className":2039},[618,653],[568,2041,2043,2062],{"className":2042},[1001,653],[568,2044,2046,2050,2054,2058],{"className":2045},[1001,653],[568,2047,2049],{"className":2048},[653],"c",[568,2051,2053],{"className":2052},[653],"o",[568,2055,2057],{"className":2056},[653],"s",[568,2059,2061],{"className":2060},[653],"h",[568,2063,2065],{"className":2064},[626],[568,2066,2068],{"className":2067},[630],[568,2069,2071],{"className":2070},[634],[568,2072,2074],{"className":2073,"style":1027},[638],[568,2075,2077,2081],{"style":2076},"top:-2.8416em;margin-right:0.0714em;",[568,2078],{"className":2079,"style":2080},[645],"height:2.5em;",[568,2082,2086],{"className":2083},[650,2084,2085,653],"reset-size3","size1",[568,2087,918],{"className":2088},[618,653],[568,2090],{"className":2091,"style":2092},[801,653],"margin-right:0.1952em;",[568,2094,595],{"className":2095},[618,622,653],[568,2097,2098,2101],{"style":1095},[568,2099],{"className":2100,"style":1086},[645],[568,2102],{"className":2103,"style":1103},[1102],[568,2105,2107,2110],{"style":2106},"top:-3.394em;",[568,2108],{"className":2109,"style":1086},[645],[568,2111,2113],{"className":2112},[650,651,652,653],[568,2114,2116],{"className":2115},[618,653],[568,2117,1840],{"className":2118},[618,653],[568,2120,1192],{"className":2121},[1191],[568,2123,2125],{"className":2124},[634],[568,2126,2129],{"className":2127,"style":2128},[638],"height:0.3713em;",[568,2130],{},[568,2132],{"className":2133},[767,1065],[568,2135],{"className":2136,"style":802},[801],[568,2138,1992],{"className":2139},[806],[568,2141],{"className":2142,"style":802},[801],[568,2144,2146,2149],{"className":2145},[609],[568,2147],{"className":2148,"style":1955},[613],[568,2150,1995],{"className":2151},[618]," ist, wächst ",[568,2154,2156,2171],{"className":2155},[571],[568,2157,2159],{"className":2158},[575],[577,2160,2161],{"xmlns":579},[581,2162,2163,2169],{},[584,2164,2165,2167],{},[590,2166,1779],{},[671,2168,880],{},[597,2170,1784],{"encoding":599},[568,2172,2174],{"className":2173,"ariaHidden":605},[604],[568,2175,2177,2180],{"className":2176},[609],[568,2178],{"className":2179,"style":1446},[613],[568,2181,1779],{"className":2182},[1001]," streng monoton.",[564,2185,2186,2187,1492,2314,2430,2431,1761],{},"Umgekehrt ergeben sich die Stammfunktionen ",[568,2188,2190,2233],{"className":2189},[571],[568,2191,2193],{"className":2192},[575],[577,2194,2195],{"xmlns":579},[581,2196,2197,2230],{},[584,2198,2199,2202,2204,2206,2208,2212,2215,2217,2219,2221,2223,2225,2227],{},[671,2200,2201],{},"∫",[590,2203,923],{},[671,2205,880],{},[590,2207,595],{},[2209,2210,2211],"mtext",{}," ",[590,2213,2214],{},"d",[590,2216,595],{},[671,2218,698],{},[590,2220,877],{},[671,2222,880],{},[590,2224,595],{},[671,2226,904],{},[590,2228,2229],{},"C",[597,2231,2232],{"encoding":599},"\\int \\cosh x\\,dx = \\sinh x + C",[568,2234,2236,2279,2303],{"className":2235,"ariaHidden":605},[604],[568,2237,2239,2243,2249,2252,2255,2258,2261,2264,2267,2270,2273,2276],{"className":2238},[609],[568,2240],{"className":2241,"style":2242},[613],"height:1.1111em;vertical-align:-0.3061em;",[568,2244,2201],{"className":2245,"style":2248},[1001,2246,2247],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[568,2250],{"className":2251,"style":1005},[801],[568,2253,923],{"className":2254},[1001],[568,2256],{"className":2257,"style":1005},[801],[568,2259,595],{"className":2260},[618,622],[568,2262],{"className":2263,"style":1005},[801],[568,2265,2214],{"className":2266},[618,622],[568,2268,595],{"className":2269},[618,622],[568,2271],{"className":2272,"style":802},[801],[568,2274,698],{"className":2275},[806],[568,2277],{"className":2278,"style":802},[801],[568,2280,2282,2285,2288,2291,2294,2297,2300],{"className":2281},[609],[568,2283],{"className":2284,"style":1655},[613],[568,2286,877],{"className":2287},[1001],[568,2289],{"className":2290,"style":1005},[801],[568,2292,595],{"className":2293},[618,622],[568,2295],{"className":2296,"style":1145},[801],[568,2298,904],{"className":2299},[1149],[568,2301],{"className":2302,"style":1145},[801],[568,2304,2306,2310],{"className":2305},[609],[568,2307],{"className":2308,"style":2309},[613],"height:0.6833em;",[568,2311,2229],{"className":2312,"style":2313},[618,622],"margin-right:0.0715em;",[568,2315,2317,2355],{"className":2316},[571],[568,2318,2320],{"className":2319},[575],[577,2321,2322],{"xmlns":579},[581,2323,2324,2352],{},[584,2325,2326,2328,2330,2332,2334,2336,2338,2340,2342,2344,2346,2348,2350],{},[671,2327,2201],{},[590,2329,877],{},[671,2331,880],{},[590,2333,595],{},[2209,2335,2211],{},[590,2337,2214],{},[590,2339,595],{},[671,2341,698],{},[590,2343,923],{},[671,2345,880],{},[590,2347,595],{},[671,2349,904],{},[590,2351,2229],{},[597,2353,2354],{"encoding":599},"\\int \\sinh x\\,dx = \\cosh x + C",[568,2356,2358,2397,2421],{"className":2357,"ariaHidden":605},[604],[568,2359,2361,2364,2367,2370,2373,2376,2379,2382,2385,2388,2391,2394],{"className":2360},[609],[568,2362],{"className":2363,"style":2242},[613],[568,2365,2201],{"className":2366,"style":2248},[1001,2246,2247],[568,2368],{"className":2369,"style":1005},[801],[568,2371,877],{"className":2372},[1001],[568,2374],{"className":2375,"style":1005},[801],[568,2377,595],{"className":2378},[618,622],[568,2380],{"className":2381,"style":1005},[801],[568,2383,2214],{"className":2384},[618,622],[568,2386,595],{"className":2387},[618,622],[568,2389],{"className":2390,"style":802},[801],[568,2392,698],{"className":2393},[806],[568,2395],{"className":2396,"style":802},[801],[568,2398,2400,2403,2406,2409,2412,2415,2418],{"className":2399},[609],[568,2401],{"className":2402,"style":1655},[613],[568,2404,923],{"className":2405},[1001],[568,2407],{"className":2408,"style":1005},[801],[568,2410,595],{"className":2411},[618,622],[568,2413],{"className":2414,"style":1145},[801],[568,2416,904],{"className":2417},[1149],[568,2419],{"className":2420,"style":1145},[801],[568,2422,2424,2427],{"className":2423},[609],[568,2425],{"className":2426,"style":2309},[613],[568,2428,2229],{"className":2429,"style":2313},[618,622],". Für die Umkehrfunktion gilt ",[568,2432,2434,2482],{"className":2433},[571],[568,2435,2437],{"className":2436},[575],[577,2438,2439],{"xmlns":579},[581,2440,2441,2479],{},[584,2442,2443,2445,2448,2450,2452,2458,2460],{},[671,2444,674],{"stretchy":673},[590,2446,2447],{"mathvariant":693},"arsinh",[671,2449,880],{},[590,2451,595],{},[587,2453,2454,2456],{},[671,2455,690],{"stretchy":673},[671,2457,695],{"mathvariant":693,"lspace":694,"rspace":694},[671,2459,698],{},[892,2461,2462,2464],{},[916,2463,1840],{},[2465,2466,2467],"msqrt",{},[584,2468,2469,2475,2477],{},[587,2470,2471,2473],{},[590,2472,595],{},[916,2474,918],{},[671,2476,904],{},[916,2478,1840],{},[597,2480,2481],{"encoding":599},"(\\operatorname{arsinh} x)' = \\frac{1}{\\sqrt{x^2 + 1}}",[568,2483,2485,2549],{"className":2484,"ariaHidden":605},[604],[568,2486,2488,2492,2495,2502,2505,2508,2540,2543,2546],{"className":2487},[609],[568,2489],{"className":2490,"style":2491},[613],"height:1.0019em;vertical-align:-0.25em;",[568,2493,674],{"className":2494},[727],[568,2496,2498],{"className":2497},[1001],[568,2499,2447],{"className":2500},[618,2501],"mathrm",[568,2503],{"className":2504,"style":1005},[801],[568,2506,595],{"className":2507},[618,622],[568,2509,2511,2514],{"className":2510},[767],[568,2512,690],{"className":2513},[767],[568,2515,2517],{"className":2516},[626],[568,2518,2520],{"className":2519},[630],[568,2521,2523],{"className":2522},[634],[568,2524,2526],{"className":2525,"style":783},[638],[568,2527,2528,2531],{"style":641},[568,2529],{"className":2530,"style":646},[645],[568,2532,2534],{"className":2533},[650,651,652,653],[568,2535,2537],{"className":2536},[618,653],[568,2538,695],{"className":2539},[618,653],[568,2541],{"className":2542,"style":802},[801],[568,2544,698],{"className":2545},[806],[568,2547],{"className":2548,"style":802},[801],[568,2550,2552,2556],{"className":2551},[609],[568,2553],{"className":2554,"style":2555},[613],"height:1.3831em;vertical-align:-0.538em;",[568,2557,2559,2562,2718],{"className":2558},[618],[568,2560],{"className":2561},[727,1065],[568,2563,2565],{"className":2564},[892],[568,2566,2568,2709],{"className":2567},[630,1072],[568,2569,2571,2706],{"className":2570},[634],[568,2572,2574,2684,2692],{"className":2573,"style":2027},[638],[568,2575,2577,2580],{"style":2576},"top:-2.5445em;",[568,2578],{"className":2579,"style":1086},[645],[568,2581,2583],{"className":2582},[650,651,652,653],[568,2584,2586],{"className":2585},[618,653],[568,2587,2590],{"className":2588},[618,2589,653],"sqrt",[568,2591,2593,2675],{"className":2592},[630,1072],[568,2594,2596,2672],{"className":2595},[634],[568,2597,2600,2649],{"className":2598,"style":2599},[638],"height:0.9221em;",[568,2601,2605,2608],{"className":2602,"style":2604},[2603],"svg-align","top:-3em;",[568,2606],{"className":2607,"style":1086},[645],[568,2609,2612,2643,2646],{"className":2610,"style":2611},[618,653],"padding-left:0.833em;",[568,2613,2615,2618],{"className":2614},[618,653],[568,2616,595],{"className":2617},[618,622,653],[568,2619,2621],{"className":2620},[626],[568,2622,2624],{"className":2623},[630],[568,2625,2627],{"className":2626},[634],[568,2628,2631],{"className":2629,"style":2630},[638],"height:0.7463em;",[568,2632,2634,2637],{"style":2633},"top:-2.786em;margin-right:0.0714em;",[568,2635],{"className":2636,"style":2080},[645],[568,2638,2640],{"className":2639},[650,2084,2085,653],[568,2641,918],{"className":2642},[618,653],[568,2644,904],{"className":2645},[1149,653],[568,2647,1840],{"className":2648},[618,653],[568,2650,2652,2655],{"style":2651},"top:-2.8821em;",[568,2653],{"className":2654,"style":1086},[645],[568,2656,2660],{"className":2657,"style":2659},[2658,653],"hide-tail","min-width:0.853em;height:1.08em;",[2661,2662,2668],"svg",{"xmlns":2663,"width":2664,"height":2665,"viewBox":2666,"preserveAspectRatio":2667},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2669,2670],"path",{"d":2671},"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",[568,2673,1192],{"className":2674},[1191],[568,2676,2678],{"className":2677},[634],[568,2679,2682],{"className":2680,"style":2681},[638],"height:0.1179em;",[568,2683],{},[568,2685,2686,2689],{"style":1095},[568,2687],{"className":2688,"style":1086},[645],[568,2690],{"className":2691,"style":1103},[1102],[568,2693,2694,2697],{"style":2106},[568,2695],{"className":2696,"style":1086},[645],[568,2698,2700],{"className":2699},[650,651,652,653],[568,2701,2703],{"className":2702},[618,653],[568,2704,1840],{"className":2705},[618,653],[568,2707,1192],{"className":2708},[1191],[568,2710,2712],{"className":2711},[634],[568,2713,2716],{"className":2714,"style":2715},[638],"height:0.538em;",[568,2717],{},[568,2719],{"className":2720},[767,1065],[559,2722,2724],{"id":2723},"beispiele","Beispiele",[564,2726,2727,2728,2819,2820,1761],{},"Mit der Kettenregel: ",[568,2729,2731,2766],{"className":2730},[571],[568,2732,2734],{"className":2733},[575],[577,2735,2736],{"xmlns":579},[581,2737,2738,2763],{},[584,2739,2740,2743,2745,2747,2749,2751,2753,2755,2757,2759,2761],{},[590,2741,2742],{},"f",[671,2744,674],{"stretchy":673},[590,2746,595],{},[671,2748,690],{"stretchy":673},[671,2750,698],{},[590,2752,923],{},[671,2754,880],{},[671,2756,674],{"stretchy":673},[916,2758,918],{},[590,2760,595],{},[671,2762,690],{"stretchy":673},[597,2764,2765],{"encoding":599},"f(x) = \\cosh(2x)",[568,2767,2769,2798],{"className":2768,"ariaHidden":605},[604],[568,2770,2772,2776,2780,2783,2786,2789,2792,2795],{"className":2771},[609],[568,2773],{"className":2774,"style":2775},[613],"height:1em;vertical-align:-0.25em;",[568,2777,2742],{"className":2778,"style":2779},[618,622],"margin-right:0.1076em;",[568,2781,674],{"className":2782},[727],[568,2784,595],{"className":2785},[618,622],[568,2787,690],{"className":2788},[767],[568,2790],{"className":2791,"style":802},[801],[568,2793,698],{"className":2794},[806],[568,2796],{"className":2797,"style":802},[801],[568,2799,2801,2804,2807,2810,2813,2816],{"className":2800},[609],[568,2802],{"className":2803,"style":2775},[613],[568,2805,923],{"className":2806},[1001],[568,2808,674],{"className":2809},[727],[568,2811,918],{"className":2812},[618],[568,2814,595],{"className":2815},[618,622],[568,2817,690],{"className":2818},[767]," hat die Ableitung ",[568,2821,2823,2863],{"className":2822},[571],[568,2824,2826],{"className":2825},[575],[577,2827,2828],{"xmlns":579},[581,2829,2830,2860],{},[584,2831,2832,2838,2840,2842,2844,2846,2848,2850,2852,2854,2856,2858],{},[587,2833,2834,2836],{},[590,2835,2742],{},[671,2837,695],{"mathvariant":693,"lspace":694,"rspace":694},[671,2839,674],{"stretchy":673},[590,2841,595],{},[671,2843,690],{"stretchy":673},[671,2845,698],{},[916,2847,918],{},[590,2849,877],{},[671,2851,880],{},[671,2853,674],{"stretchy":673},[916,2855,918],{},[590,2857,595],{},[671,2859,690],{"stretchy":673},[597,2861,2862],{"encoding":599},"f'(x) = 2\\sinh(2x)",[568,2864,2866,2922],{"className":2865,"ariaHidden":605},[604],[568,2867,2869,2872,2904,2907,2910,2913,2916,2919],{"className":2868},[609],[568,2870],{"className":2871,"style":2491},[613],[568,2873,2875,2878],{"className":2874},[618],[568,2876,2742],{"className":2877,"style":2779},[618,622],[568,2879,2881],{"className":2880},[626],[568,2882,2884],{"className":2883},[630],[568,2885,2887],{"className":2886},[634],[568,2888,2890],{"className":2889,"style":783},[638],[568,2891,2892,2895],{"style":641},[568,2893],{"className":2894,"style":646},[645],[568,2896,2898],{"className":2897},[650,651,652,653],[568,2899,2901],{"className":2900},[618,653],[568,2902,695],{"className":2903},[618,653],[568,2905,674],{"className":2906},[727],[568,2908,595],{"className":2909},[618,622],[568,2911,690],{"className":2912},[767],[568,2914],{"className":2915,"style":802},[801],[568,2917,698],{"className":2918},[806],[568,2920],{"className":2921,"style":802},[801],[568,2923,2925,2928,2931,2934,2937,2940,2943,2946],{"className":2924},[609],[568,2926],{"className":2927,"style":2775},[613],[568,2929,918],{"className":2930},[618],[568,2932],{"className":2933,"style":1005},[801],[568,2935,877],{"className":2936},[1001],[568,2938,674],{"className":2939},[727],[568,2941,918],{"className":2942},[618],[568,2944,595],{"className":2945},[618,622],[568,2947,690],{"className":2948},[767],[564,2950,2951,2952,2819,3036,1761],{},"Mit der Produktregel: ",[568,2953,2955,2985],{"className":2954},[571],[568,2956,2958],{"className":2957},[575],[577,2959,2960],{"xmlns":579},[581,2961,2962,2982],{},[584,2963,2964,2966,2968,2970,2972,2974,2976,2978,2980],{},[590,2965,2742],{},[671,2967,674],{"stretchy":673},[590,2969,595],{},[671,2971,690],{"stretchy":673},[671,2973,698],{},[590,2975,595],{},[590,2977,877],{},[671,2979,880],{},[590,2981,595],{},[597,2983,2984],{"encoding":599},"f(x) = x \\sinh x",[568,2986,2988,3015],{"className":2987,"ariaHidden":605},[604],[568,2989,2991,2994,2997,3000,3003,3006,3009,3012],{"className":2990},[609],[568,2992],{"className":2993,"style":2775},[613],[568,2995,2742],{"className":2996,"style":2779},[618,622],[568,2998,674],{"className":2999},[727],[568,3001,595],{"className":3002},[618,622],[568,3004,690],{"className":3005},[767],[568,3007],{"className":3008,"style":802},[801],[568,3010,698],{"className":3011},[806],[568,3013],{"className":3014,"style":802},[801],[568,3016,3018,3021,3024,3027,3030,3033],{"className":3017},[609],[568,3019],{"className":3020,"style":1446},[613],[568,3022,595],{"className":3023},[618,622],[568,3025],{"className":3026,"style":1005},[801],[568,3028,877],{"className":3029},[1001],[568,3031],{"className":3032,"style":1005},[801],[568,3034,595],{"className":3035},[618,622],[568,3037,3039,3081],{"className":3038},[571],[568,3040,3042],{"className":3041},[575],[577,3043,3044],{"xmlns":579},[581,3045,3046,3078],{},[584,3047,3048,3054,3056,3058,3060,3062,3064,3066,3068,3070,3072,3074,3076],{},[587,3049,3050,3052],{},[590,3051,2742],{},[671,3053,695],{"mathvariant":693,"lspace":694,"rspace":694},[671,3055,674],{"stretchy":673},[590,3057,595],{},[671,3059,690],{"stretchy":673},[671,3061,698],{},[590,3063,877],{},[671,3065,880],{},[590,3067,595],{},[671,3069,904],{},[590,3071,595],{},[590,3073,923],{},[671,3075,880],{},[590,3077,595],{},[597,3079,3080],{"encoding":599},"f'(x) = \\sinh x + x \\cosh x",[568,3082,3084,3140,3164],{"className":3083,"ariaHidden":605},[604],[568,3085,3087,3090,3122,3125,3128,3131,3134,3137],{"className":3086},[609],[568,3088],{"className":3089,"style":2491},[613],[568,3091,3093,3096],{"className":3092},[618],[568,3094,2742],{"className":3095,"style":2779},[618,622],[568,3097,3099],{"className":3098},[626],[568,3100,3102],{"className":3101},[630],[568,3103,3105],{"className":3104},[634],[568,3106,3108],{"className":3107,"style":783},[638],[568,3109,3110,3113],{"style":641},[568,3111],{"className":3112,"style":646},[645],[568,3114,3116],{"className":3115},[650,651,652,653],[568,3117,3119],{"className":3118},[618,653],[568,3120,695],{"className":3121},[618,653],[568,3123,674],{"className":3124},[727],[568,3126,595],{"className":3127},[618,622],[568,3129,690],{"className":3130},[767],[568,3132],{"className":3133,"style":802},[801],[568,3135,698],{"className":3136},[806],[568,3138],{"className":3139,"style":802},[801],[568,3141,3143,3146,3149,3152,3155,3158,3161],{"className":3142},[609],[568,3144],{"className":3145,"style":1655},[613],[568,3147,877],{"className":3148},[1001],[568,3150],{"className":3151,"style":1005},[801],[568,3153,595],{"className":3154},[618,622],[568,3156],{"className":3157,"style":1145},[801],[568,3159,904],{"className":3160},[1149],[568,3162],{"className":3163,"style":1145},[801],[568,3165,3167,3170,3173,3176,3179,3182],{"className":3166},[609],[568,3168],{"className":3169,"style":1446},[613],[568,3171,595],{"className":3172},[618,622],[568,3174],{"className":3175,"style":1005},[801],[568,3177,923],{"className":3178},[1001],[568,3180],{"className":3181,"style":1005},[801],[568,3183,595],{"className":3184},[618,622],[564,3186,3187,3188,1761],{},"Ein Integral: ",[568,3189,3191,3246],{"className":3190},[571],[568,3192,3194],{"className":3193},[575],[577,3195,3196],{"xmlns":579},[581,3197,3198,3243],{},[584,3199,3200,3209,3211,3213,3215,3217,3219,3221,3223,3225,3227,3229,3231,3233,3235,3237,3240],{},[3201,3202,3203,3205,3207],"msubsup",{},[671,3204,2201],{},[916,3206,1995],{},[916,3208,1840],{},[590,3210,923],{},[671,3212,880],{},[590,3214,595],{},[2209,3216,2211],{},[590,3218,2214],{},[590,3220,595],{},[671,3222,698],{},[590,3224,877],{},[671,3226,880],{},[916,3228,1840],{},[671,3230,683],{},[590,3232,877],{},[671,3234,880],{},[916,3236,1995],{},[671,3238,3239],{},"≈",[916,3241,3242],{},"1,1752",[597,3244,3245],{"encoding":599},"\\int_0^1 \\cosh x\\,dx = \\sinh 1 - \\sinh 0 \\approx 1{,}1752",[568,3247,3249,3341,3365,3389],{"className":3248,"ariaHidden":605},[604],[568,3250,3252,3256,3311,3314,3317,3320,3323,3326,3329,3332,3335,3338],{"className":3251},[609],[568,3253],{"className":3254,"style":3255},[613],"height:1.3648em;vertical-align:-0.3558em;",[568,3257,3259,3262],{"className":3258},[1001],[568,3260,2201],{"className":3261,"style":2248},[1001,2246,2247],[568,3263,3265],{"className":3264},[626],[568,3266,3268,3302],{"className":3267},[630,1072],[568,3269,3271,3299],{"className":3270},[634],[568,3272,3275,3287],{"className":3273,"style":3274},[638],"height:1.009em;",[568,3276,3278,3281],{"style":3277},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[568,3279],{"className":3280,"style":646},[645],[568,3282,3284],{"className":3283},[650,651,652,653],[568,3285,1995],{"className":3286},[618,653],[568,3288,3290,3293],{"style":3289},"top:-3.2579em;margin-right:0.05em;",[568,3291],{"className":3292,"style":646},[645],[568,3294,3296],{"className":3295},[650,651,652,653],[568,3297,1840],{"className":3298},[618,653],[568,3300,1192],{"className":3301},[1191],[568,3303,3305],{"className":3304},[634],[568,3306,3309],{"className":3307,"style":3308},[638],"height:0.3558em;",[568,3310],{},[568,3312],{"className":3313,"style":1005},[801],[568,3315,923],{"className":3316},[1001],[568,3318],{"className":3319,"style":1005},[801],[568,3321,595],{"className":3322},[618,622],[568,3324],{"className":3325,"style":1005},[801],[568,3327,2214],{"className":3328},[618,622],[568,3330,595],{"className":3331},[618,622],[568,3333],{"className":3334,"style":802},[801],[568,3336,698],{"className":3337},[806],[568,3339],{"className":3340,"style":802},[801],[568,3342,3344,3347,3350,3353,3356,3359,3362],{"className":3343},[609],[568,3345],{"className":3346,"style":1655},[613],[568,3348,877],{"className":3349},[1001],[568,3351],{"className":3352,"style":1005},[801],[568,3354,1840],{"className":3355},[618],[568,3357],{"className":3358,"style":1145},[801],[568,3360,683],{"className":3361},[1149],[568,3363],{"className":3364,"style":1145},[801],[568,3366,3368,3371,3374,3377,3380,3383,3386],{"className":3367},[609],[568,3369],{"className":3370,"style":1446},[613],[568,3372,877],{"className":3373},[1001],[568,3375],{"className":3376,"style":1005},[801],[568,3378,1995],{"className":3379},[618],[568,3381],{"className":3382,"style":802},[801],[568,3384,3239],{"className":3385},[806],[568,3387],{"className":3388,"style":802},[801],[568,3390,3392,3396,3399,3405],{"className":3391},[609],[568,3393],{"className":3394,"style":3395},[613],"height:0.8389em;vertical-align:-0.1944em;",[568,3397,1840],{"className":3398},[618],[568,3400,3402],{"className":3401},[618],[568,3403,930],{"className":3404},[1232],[568,3406,3408],{"className":3407},[618],"1752",[559,3410,3412],{"id":3411},"typische-fehler","Typische Fehler",[3414,3415,3416,3666,3866],"ul",{},[3417,3418,3419,3420,3543,3544,1761],"li",{},"Das Minuszeichen von ",[568,3421,3423,3459],{"className":3422},[571],[568,3424,3426],{"className":3425},[575],[577,3427,3428],{"xmlns":579},[581,3429,3430,3456],{},[584,3431,3432,3434,3436,3438,3440,3446,3448,3450,3452,3454],{},[671,3433,674],{"stretchy":673},[590,3435,1507],{},[671,3437,880],{},[590,3439,595],{},[587,3441,3442,3444],{},[671,3443,690],{"stretchy":673},[671,3445,695],{"mathvariant":693,"lspace":694,"rspace":694},[671,3447,698],{},[671,3449,683],{},[590,3451,1473],{},[671,3453,880],{},[590,3455,595],{},[597,3457,3458],{"encoding":599},"(\\cos x)' = -\\sin x",[568,3460,3462,3521],{"className":3461,"ariaHidden":605},[604],[568,3463,3465,3468,3471,3474,3477,3480,3512,3515,3518],{"className":3464},[609],[568,3466],{"className":3467,"style":2491},[613],[568,3469,674],{"className":3470},[727],[568,3472,1507],{"className":3473},[1001],[568,3475],{"className":3476,"style":1005},[801],[568,3478,595],{"className":3479},[618,622],[568,3481,3483,3486],{"className":3482},[767],[568,3484,690],{"className":3485},[767],[568,3487,3489],{"className":3488},[626],[568,3490,3492],{"className":3491},[630],[568,3493,3495],{"className":3494},[634],[568,3496,3498],{"className":3497,"style":783},[638],[568,3499,3500,3503],{"style":641},[568,3501],{"className":3502,"style":646},[645],[568,3504,3506],{"className":3505},[650,651,652,653],[568,3507,3509],{"className":3508},[618,653],[568,3510,695],{"className":3511},[618,653],[568,3513],{"className":3514,"style":802},[801],[568,3516,698],{"className":3517},[806],[568,3519],{"className":3520,"style":802},[801],[568,3522,3524,3528,3531,3534,3537,3540],{"className":3523},[609],[568,3525],{"className":3526,"style":3527},[613],"height:0.7512em;vertical-align:-0.0833em;",[568,3529,683],{"className":3530},[618],[568,3532],{"className":3533,"style":1005},[801],[568,3535,1473],{"className":3536},[1001],[568,3538],{"className":3539,"style":1005},[801],[568,3541,595],{"className":3542},[618,622]," übernehmen. Richtig ist ",[568,3545,3547,3583],{"className":3546},[571],[568,3548,3550],{"className":3549},[575],[577,3551,3552],{"xmlns":579},[581,3553,3554,3580],{},[584,3555,3556,3558,3560,3562,3564,3570,3572,3574,3576,3578],{},[671,3557,674],{"stretchy":673},[590,3559,923],{},[671,3561,880],{},[590,3563,595],{},[587,3565,3566,3568],{},[671,3567,690],{"stretchy":673},[671,3569,695],{"mathvariant":693,"lspace":694,"rspace":694},[671,3571,698],{},[671,3573,904],{},[590,3575,877],{},[671,3577,880],{},[590,3579,595],{},[597,3581,3582],{"encoding":599},"(\\cosh x)' = +\\sinh x",[568,3584,3586,3645],{"className":3585,"ariaHidden":605},[604],[568,3587,3589,3592,3595,3598,3601,3604,3636,3639,3642],{"className":3588},[609],[568,3590],{"className":3591,"style":2491},[613],[568,3593,674],{"className":3594},[727],[568,3596,923],{"className":3597},[1001],[568,3599],{"className":3600,"style":1005},[801],[568,3602,595],{"className":3603},[618,622],[568,3605,3607,3610],{"className":3606},[767],[568,3608,690],{"className":3609},[767],[568,3611,3613],{"className":3612},[626],[568,3614,3616],{"className":3615},[630],[568,3617,3619],{"className":3618},[634],[568,3620,3622],{"className":3621,"style":783},[638],[568,3623,3624,3627],{"style":641},[568,3625],{"className":3626,"style":646},[645],[568,3628,3630],{"className":3629},[650,651,652,653],[568,3631,3633],{"className":3632},[618,653],[568,3634,695],{"className":3635},[618,653],[568,3637],{"className":3638,"style":802},[801],[568,3640,698],{"className":3641},[806],[568,3643],{"className":3644,"style":802},[801],[568,3646,3648,3651,3654,3657,3660,3663],{"className":3647},[609],[568,3649],{"className":3650,"style":1655},[613],[568,3652,904],{"className":3653},[618],[568,3655],{"className":3656,"style":1005},[801],[568,3658,877],{"className":3659},[1001],[568,3661],{"className":3662,"style":1005},[801],[568,3664,595],{"className":3665},[618,622],[3417,3667,3668,3669,1624,3815,1761],{},"Die innere Ableitung vergessen: ",[568,3670,3672,3720],{"className":3671},[571],[568,3673,3675],{"className":3674},[575],[577,3676,3677],{"xmlns":579},[581,3678,3679,3717],{},[584,3680,3681,3683,3685,3687,3689,3691,3693,3695,3701,3703,3705,3707,3709,3711,3713,3715],{},[671,3682,674],{"stretchy":673},[590,3684,923],{},[671,3686,880],{},[671,3688,674],{"stretchy":673},[916,3690,918],{},[590,3692,595],{},[671,3694,690],{"stretchy":673},[587,3696,3697,3699],{},[671,3698,690],{"stretchy":673},[671,3700,695],{"mathvariant":693,"lspace":694,"rspace":694},[671,3702,698],{},[916,3704,918],{},[590,3706,877],{},[671,3708,880],{},[671,3710,674],{"stretchy":673},[916,3712,918],{},[590,3714,595],{},[671,3716,690],{"stretchy":673},[597,3718,3719],{"encoding":599},"(\\cosh(2x))' = 2\\sinh(2x)",[568,3721,3723,3788],{"className":3722,"ariaHidden":605},[604],[568,3724,3726,3729,3732,3735,3738,3741,3744,3747,3779,3782,3785],{"className":3725},[609],[568,3727],{"className":3728,"style":2491},[613],[568,3730,674],{"className":3731},[727],[568,3733,923],{"className":3734},[1001],[568,3736,674],{"className":3737},[727],[568,3739,918],{"className":3740},[618],[568,3742,595],{"className":3743},[618,622],[568,3745,690],{"className":3746},[767],[568,3748,3750,3753],{"className":3749},[767],[568,3751,690],{"className":3752},[767],[568,3754,3756],{"className":3755},[626],[568,3757,3759],{"className":3758},[630],[568,3760,3762],{"className":3761},[634],[568,3763,3765],{"className":3764,"style":783},[638],[568,3766,3767,3770],{"style":641},[568,3768],{"className":3769,"style":646},[645],[568,3771,3773],{"className":3772},[650,651,652,653],[568,3774,3776],{"className":3775},[618,653],[568,3777,695],{"className":3778},[618,653],[568,3780],{"className":3781,"style":802},[801],[568,3783,698],{"className":3784},[806],[568,3786],{"className":3787,"style":802},[801],[568,3789,3791,3794,3797,3800,3803,3806,3809,3812],{"className":3790},[609],[568,3792],{"className":3793,"style":2775},[613],[568,3795,918],{"className":3796},[618],[568,3798],{"className":3799,"style":1005},[801],[568,3801,877],{"className":3802},[1001],[568,3804,674],{"className":3805},[727],[568,3807,918],{"className":3808},[618],[568,3810,595],{"className":3811},[618,622],[568,3813,690],{"className":3814},[767],[568,3816,3818,3842],{"className":3817},[571],[568,3819,3821],{"className":3820},[575],[577,3822,3823],{"xmlns":579},[581,3824,3825,3839],{},[584,3826,3827,3829,3831,3833,3835,3837],{},[590,3828,877],{},[671,3830,880],{},[671,3832,674],{"stretchy":673},[916,3834,918],{},[590,3836,595],{},[671,3838,690],{"stretchy":673},[597,3840,3841],{"encoding":599},"\\sinh(2x)",[568,3843,3845],{"className":3844,"ariaHidden":605},[604],[568,3846,3848,3851,3854,3857,3860,3863],{"className":3847},[609],[568,3849],{"className":3850,"style":2775},[613],[568,3852,877],{"className":3853},[1001],[568,3855,674],{"className":3856},[727],[568,3858,918],{"className":3859},[618],[568,3861,595],{"className":3862},[618,622],[568,3864,690],{"className":3865},[767],[3417,3867,3868,4037,4038,4068],{},[568,3869,3871,3915],{"className":3870},[571],[568,3872,3874],{"className":3873},[575],[577,3875,3876],{"xmlns":579},[581,3877,3878,3912],{},[584,3879,3880,3882,3884,3886,3888,3894,3896,3898,3900,3910],{},[671,3881,674],{"stretchy":673},[590,3883,1779],{},[671,3885,880],{},[590,3887,595],{},[587,3889,3890,3892],{},[671,3891,690],{"stretchy":673},[671,3893,695],{"mathvariant":693,"lspace":694,"rspace":694},[671,3895,698],{},[916,3897,1840],{},[671,3899,904],{},[587,3901,3902,3908],{},[584,3903,3904,3906],{},[590,3905,1779],{},[671,3907,880],{},[916,3909,918],{},[590,3911,595],{},[597,3913,3914],{"encoding":599},"(\\tanh x)' = 1 + \\tanh^2 x",[568,3916,3918,3977,3996],{"className":3917,"ariaHidden":605},[604],[568,3919,3921,3924,3927,3930,3933,3936,3968,3971,3974],{"className":3920},[609],[568,3922],{"className":3923,"style":2491},[613],[568,3925,674],{"className":3926},[727],[568,3928,1779],{"className":3929},[1001],[568,3931],{"className":3932,"style":1005},[801],[568,3934,595],{"className":3935},[618,622],[568,3937,3939,3942],{"className":3938},[767],[568,3940,690],{"className":3941},[767],[568,3943,3945],{"className":3944},[626],[568,3946,3948],{"className":3947},[630],[568,3949,3951],{"className":3950},[634],[568,3952,3954],{"className":3953,"style":783},[638],[568,3955,3956,3959],{"style":641},[568,3957],{"className":3958,"style":646},[645],[568,3960,3962],{"className":3961},[650,651,652,653],[568,3963,3965],{"className":3964},[618,653],[568,3966,695],{"className":3967},[618,653],[568,3969],{"className":3970,"style":802},[801],[568,3972,698],{"className":3973},[806],[568,3975],{"className":3976,"style":802},[801],[568,3978,3980,3984,3987,3990,3993],{"className":3979},[609],[568,3981],{"className":3982,"style":3983},[613],"height:0.7278em;vertical-align:-0.0833em;",[568,3985,1840],{"className":3986},[618],[568,3988],{"className":3989,"style":1145},[801],[568,3991,904],{"className":3992},[1149],[568,3994],{"className":3995,"style":1145},[801],[568,3997,3999,4002,4031,4034],{"className":3998},[609],[568,4000],{"className":4001,"style":1872},[613],[568,4003,4005,4008],{"className":4004},[1001],[568,4006,1779],{"className":4007},[1001],[568,4009,4011],{"className":4010},[626],[568,4012,4014],{"className":4013},[630],[568,4015,4017],{"className":4016},[634],[568,4018,4020],{"className":4019,"style":1872},[638],[568,4021,4022,4025],{"style":1593},[568,4023],{"className":4024,"style":646},[645],[568,4026,4028],{"className":4027},[650,651,652,653],[568,4029,918],{"className":4030},[618,653],[568,4032],{"className":4033,"style":1005},[801],[568,4035,595],{"className":4036},[618,622]," schreiben. Das ist die Ableitung des gewöhnlichen Tangens; beim ",[568,4039,4041,4056],{"className":4040},[571],[568,4042,4044],{"className":4043},[575],[577,4045,4046],{"xmlns":579},[581,4047,4048,4054],{},[584,4049,4050,4052],{},[590,4051,1779],{},[671,4053,880],{},[597,4055,1784],{"encoding":599},[568,4057,4059],{"className":4058,"ariaHidden":605},[604],[568,4060,4062,4065],{"className":4061},[609],[568,4063],{"className":4064,"style":1446},[613],[568,4066,1779],{"className":4067},[1001]," steht ein Minus.",{"title":4070,"searchDepth":4071,"depth":4071,"links":4072},"",2,[4073,4074,4075],{"id":561,"depth":4071,"text":562},{"id":2723,"depth":4071,"text":2724},{"id":3411,"depth":4071,"text":3412},[4077,4079,4081,4083,4086,4088,4090,4092,4095],{"lhs":4078,"rhs":1995},"round((sinh(x + 1e-5) - sinh(x - 1e-5))\u002F2e-5 - cosh(x), 6)",{"lhs":4080,"rhs":1995},"round((cosh(x + 1e-5) - cosh(x - 1e-5))\u002F2e-5 - sinh(x), 6)",{"lhs":4082,"rhs":1995},"round((tanh(x + 1e-5) - tanh(x - 1e-5))\u002F2e-5 - 1\u002Fcosh(x)^2, 6)",{"lhs":4084,"rhs":4085},"1\u002Fcosh(x)^2","1 - tanh(x)^2",{"lhs":4087,"rhs":1995},"round((asinh(x + 1e-5) - asinh(x - 1e-5))\u002F2e-5 - 1\u002Fsqrt(x^2 + 1), 6)",{"lhs":4089,"rhs":1995},"round((cosh(2*(x + 1e-5)) - cosh(2*(x - 1e-5)))\u002F2e-5 - 2*sinh(2*x), 6)",{"lhs":4091,"rhs":1995},"round(((x + 1e-5)*sinh(x + 1e-5) - (x - 1e-5)*sinh(x - 1e-5))\u002F2e-5 - (sinh(x) + x*cosh(x)), 6)",{"lhs":4093,"rhs":4094},"round(sum(map(0:999, f(k) = cosh((k + 0.5)\u002F1000)))\u002F1000, 4)","round(sinh(1), 4)",{"lhs":4094,"rhs":4096},"1.1752",null,"md","derivative-hyperbolic","(\\sinh x)' = \\cosh x,\\quad (\\cosh x)' = \\sinh x,\\quad (\\tanh x)' = \\frac{1}{\\cosh^2 x} = 1 - \\tanh^2 x","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>sinh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>cosh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>cosh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>sinh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>tanh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmrow>\u003Cmsup>\u003Cmrow>\u003Cmi>cosh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmrow>\u003Cmi>tanh\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(\\sinh x)' = \\cosh x,\\quad (\\cosh x)' = \\sinh x,\\quad (\\tanh x)' = \\frac{1}{\\cosh^2 x} = 1 - \\tanh^2 x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0519em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mop\">sinh\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\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=\"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:1.0519em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">cosh\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mop\">cosh\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\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=\"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:1.0519em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sinh\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mop\">tanh\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\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=\"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:2.1099em;vertical-align:-0.7884em;\">\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:-2.2116em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">\u003Cspan class=\"mop\">cosh\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8984em;\">\u003Cspan style=\"top:-3.1473em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7884em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8984em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop\">tanh\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8984em;\">\u003Cspan style=\"top:-3.1473em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-hyperbelfunktionen",[],[4108,4109,4110,4111],"hyperbolic-functions","hyperbolic-identity","derivative-exp","chain-rule",{"title":548,"description":4070},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-hyperbelfunktionen","sinh und cosh leiten sich gegenseitig ab, ohne Vorzeichenwechsel; tanh hat die Ableitung 1 − tanh².",[4116,4117,4118,4119,4120],"ableitung","hyperbelfunktionen","sinus hyperbolicus","kosinus hyperbolicus","tangens hyperbolicus",[4122,4125],{"symbol":595,"meaning":4123,"symbolHtml":4124},"reelle Zahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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