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",[569,1161,1163,1186],{"className":1162},[572],[569,1164,1166],{"className":1165},[576],[578,1167,1168],{"xmlns":580},[582,1169,1170,1183],{},[585,1171,1172,1181],{},[1018,1173,1174,1177],{},[588,1175,1176],{},"D",[1178,1179,1180],"mn",{},"1",[588,1182,590],{},[610,1184,1185],{"encoding":612},"D_1 f",[569,1187,1189],{"className":1188,"ariaHidden":601},[617],[569,1190,1192,1195,1238],{"className":1191},[621],[569,1193],{"className":1194,"style":1036},[625],[569,1196,1198,1202],{"className":1197},[630],[569,1199,1176],{"className":1200,"style":1201},[630,631],"margin-right:0.0278em;",[569,1203,1205],{"className":1204},[1046],[569,1206,1208,1230],{"className":1207},[718,719],[569,1209,1211,1227],{"className":1210},[723],[569,1212,1215],{"className":1213,"style":1214},[727],"height:0.3011em;",[569,1216,1218,1221],{"style":1217},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[569,1219],{"className":1220,"style":1063},[735],[569,1222,1224],{"className":1223},[740,741,742,743],[569,1225,1180],{"className":1226},[630,743],[569,1228,787],{"className":1229},[786],[569,1231,1233],{"className":1232},[723],[569,1234,1236],{"className":1235,"style":1079},[727],[569,1237],{},[569,1239,590],{"className":1240,"style":632},[630,631],".",[565,1243,1244,1245,1428,1429,1241],{},"Geometrisch ist ",[569,1246,1248,1285],{"className":1247},[572],[569,1249,1251],{"className":1250},[576],[578,1252,1253],{"xmlns":580},[582,1254,1255,1282],{},[585,1256,1257,1263,1265,1272,1274,1280],{},[1018,1258,1259,1261],{},[588,1260,590],{},[588,1262,598],{},[592,1264,595],{"stretchy":594},[1018,1266,1267,1269],{},[588,1268,598],{},[1178,1270,1271],{},"0",[592,1273,602],{"separator":601},[1018,1275,1276,1278],{},[588,1277,605],{},[1178,1279,1271],{},[592,1281,608],{"stretchy":594},[610,1283,1284],{"encoding":612},"f_x(x_0, y_0)",[569,1286,1288],{"className":1287,"ariaHidden":601},[617],[569,1289,1291,1294,1334,1337,1378,1381,1384,1425],{"className":1290},[621],[569,1292],{"className":1293,"style":626},[625],[569,1295,1297,1300],{"className":1296},[630],[569,1298,590],{"className":1299,"style":632},[630,631],[569,1301,1303],{"className":1302},[1046],[569,1304,1306,1326],{"className":1305},[718,719],[569,1307,1309,1323],{"className":1308},[723],[569,1310,1312],{"className":1311,"style":1056},[727],[569,1313,1314,1317],{"style":1059},[569,1315],{"className":1316,"style":1063},[735],[569,1318,1320],{"className":1319},[740,741,742,743],[569,1321,598],{"className":1322},[630,631,743],[569,1324,787],{"className":1325},[786],[569,1327,1329],{"className":1328},[723],[569,1330,1332],{"className":1331,"style":1079},[727],[569,1333],{},[569,1335,595],{"className":1336},[636],[569,1338,1340,1343],{"className":1339},[630],[569,1341,598],{"className":1342},[630,631],[569,1344,1346],{"className":1345},[1046],[569,1347,1349,1370],{"className":1348},[718,719],[569,1350,1352,1367],{"className":1351},[723],[569,1353,1355],{"className":1354,"style":1214},[727],[569,1356,1358,1361],{"style":1357},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[569,1359],{"className":1360,"style":1063},[735],[569,1362,1364],{"className":1363},[740,741,742,743],[569,1365,1271],{"className":1366},[630,743],[569,1368,787],{"className":1369},[786],[569,1371,1373],{"className":1372},[723],[569,1374,1376],{"className":1375,"style":1079},[727],[569,1377],{},[569,1379,602],{"className":1380},[643],[569,1382],{"className":1383,"style":648},[647],[569,1385,1387,1390],{"className":1386},[630],[569,1388,605],{"className":1389,"style":652},[630,631],[569,1391,1393],{"className":1392},[1046],[569,1394,1396,1417],{"className":1395},[718,719],[569,1397,1399,1414],{"className":1398},[723],[569,1400,1402],{"className":1401,"style":1214},[727],[569,1403,1405,1408],{"style":1404},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[569,1406],{"className":1407,"style":1063},[735],[569,1409,1411],{"className":1410},[740,741,742,743],[569,1412,1271],{"className":1413},[630,743],[569,1415,787],{"className":1416},[786],[569,1418,1420],{"className":1419},[723],[569,1421,1423],{"className":1422,"style":1079},[727],[569,1424],{},[569,1426,608],{"className":1427},[656]," die Steigung der Schnittkurve des Graphen mit der Ebene ",[569,1430,1432,1455],{"className":1431},[572],[569,1433,1435],{"className":1434},[576],[578,1436,1437],{"xmlns":580},[582,1438,1439,1452],{},[585,1440,1441,1443,1446],{},[588,1442,605],{},[592,1444,1445],{},"=",[1018,1447,1448,1450],{},[588,1449,605],{},[1178,1451,1271],{},[610,1453,1454],{"encoding":612},"y = y_0",[569,1456,1458,1478],{"className":1457,"ariaHidden":601},[617],[569,1459,1461,1464,1467,1471,1475],{"className":1460},[621],[569,1462],{"className":1463,"style":826},[625],[569,1465,605],{"className":1466,"style":652},[630,631],[569,1468],{"className":1469,"style":1470},[647],"margin-right:0.2778em;",[569,1472,1445],{"className":1473},[1474],"mrel",[569,1476],{"className":1477,"style":1470},[647],[569,1479,1481,1484],{"className":1480},[621],[569,1482],{"className":1483,"style":826},[625],[569,1485,1487,1490],{"className":1486},[630],[569,1488,605],{"className":1489,"style":652},[630,631],[569,1491,1493],{"className":1492},[1046],[569,1494,1496,1516],{"className":1495},[718,719],[569,1497,1499,1513],{"className":1498},[723],[569,1500,1502],{"className":1501,"style":1214},[727],[569,1503,1504,1507],{"style":1404},[569,1505],{"className":1506,"style":1063},[735],[569,1508,1510],{"className":1509},[740,741,742,743],[569,1511,1271],{"className":1512},[630,743],[569,1514,787],{"className":1515},[786],[569,1517,1519],{"className":1518},[723],[569,1520,1522],{"className":1521,"style":1079},[727],[569,1523],{},[565,1525,1526,1527,1530,1531,1082,1609,1691,1692,1772,1773,1775,1776,1929,1930,1959],{},"Leitet man noch einmal ab, entstehen ",[659,1528,1529],{},"höhere partielle Ableitungen"," wie ",[569,1532,1534,1556],{"className":1533},[572],[569,1535,1537],{"className":1536},[576],[578,1538,1539],{"xmlns":580},[582,1540,1541,1553],{},[585,1542,1543],{},[1018,1544,1545,1547],{},[588,1546,590],{},[585,1548,1549,1551],{},[588,1550,598],{},[588,1552,598],{},[610,1554,1555],{"encoding":612},"f_{xx}",[569,1557,1559],{"className":1558,"ariaHidden":601},[617],[569,1560,1562,1565],{"className":1561},[621],[569,1563],{"className":1564,"style":1036},[625],[569,1566,1568,1571],{"className":1567},[630],[569,1569,590],{"className":1570,"style":632},[630,631],[569,1572,1574],{"className":1573},[1046],[569,1575,1577,1601],{"className":1576},[718,719],[569,1578,1580,1598],{"className":1579},[723],[569,1581,1583],{"className":1582,"style":1056},[727],[569,1584,1585,1588],{"style":1059},[569,1586],{"className":1587,"style":1063},[735],[569,1589,1591],{"className":1590},[740,741,742,743],[569,1592,1594],{"className":1593},[630,743],[569,1595,1597],{"className":1596},[630,631,743],"xx",[569,1599,787],{"className":1600},[786],[569,1602,1604],{"className":1603},[723],[569,1605,1607],{"className":1606,"style":1079},[727],[569,1608],{},[569,1610,1612,1634],{"className":1611},[572],[569,1613,1615],{"className":1614},[576],[578,1616,1617],{"xmlns":580},[582,1618,1619,1631],{},[585,1620,1621],{},[1018,1622,1623,1625],{},[588,1624,590],{},[585,1626,1627,1629],{},[588,1628,598],{},[588,1630,605],{},[610,1632,1633],{"encoding":612},"f_{xy}",[569,1635,1637],{"className":1636,"ariaHidden":601},[617],[569,1638,1640,1644],{"className":1639},[621],[569,1641],{"className":1642,"style":1643},[625],"height:0.9805em;vertical-align:-0.2861em;",[569,1645,1647,1650],{"className":1646},[630],[569,1648,590],{"className":1649,"style":632},[630,631],[569,1651,1653],{"className":1652},[1046],[569,1654,1656,1682],{"className":1655},[718,719],[569,1657,1659,1679],{"className":1658},[723],[569,1660,1662],{"className":1661,"style":1056},[727],[569,1663,1664,1667],{"style":1059},[569,1665],{"className":1666,"style":1063},[735],[569,1668,1670],{"className":1669},[740,741,742,743],[569,1671,1673,1676],{"className":1672},[630,743],[569,1674,598],{"className":1675},[630,631,743],[569,1677,605],{"className":1678,"style":652},[630,631,743],[569,1680,787],{"className":1681},[786],[569,1683,1685],{"className":1684},[723],[569,1686,1689],{"className":1687,"style":1688},[727],"height:0.2861em;",[569,1690],{}," und ",[569,1693,1695,1717],{"className":1694},[572],[569,1696,1698],{"className":1697},[576],[578,1699,1700],{"xmlns":580},[582,1701,1702,1714],{},[585,1703,1704],{},[1018,1705,1706,1708],{},[588,1707,590],{},[585,1709,1710,1712],{},[588,1711,605],{},[588,1713,605],{},[610,1715,1716],{"encoding":612},"f_{yy}",[569,1718,1720],{"className":1719,"ariaHidden":601},[617],[569,1721,1723,1726],{"className":1722},[621],[569,1724],{"className":1725,"style":1643},[625],[569,1727,1729,1732],{"className":1728},[630],[569,1730,590],{"className":1731,"style":632},[630,631],[569,1733,1735],{"className":1734},[1046],[569,1736,1738,1764],{"className":1737},[718,719],[569,1739,1741,1761],{"className":1740},[723],[569,1742,1744],{"className":1743,"style":1056},[727],[569,1745,1746,1749],{"style":1059},[569,1747],{"className":1748,"style":1063},[735],[569,1750,1752],{"className":1751},[740,741,742,743],[569,1753,1755,1758],{"className":1754},[630,743],[569,1756,605],{"className":1757,"style":652},[630,631,743],[569,1759,605],{"className":1760,"style":652},[630,631,743],[569,1762,787],{"className":1763},[786],[569,1765,1767],{"className":1766},[723],[569,1768,1770],{"className":1769,"style":1688},[727],[569,1771],{},". Nach dem ",[659,1774,554],{}," gilt ",[569,1777,1779,1813],{"className":1778},[572],[569,1780,1782],{"className":1781},[576],[578,1783,1784],{"xmlns":580},[582,1785,1786,1810],{},[585,1787,1788,1798,1800],{},[1018,1789,1790,1792],{},[588,1791,590],{},[585,1793,1794,1796],{},[588,1795,598],{},[588,1797,605],{},[592,1799,1445],{},[1018,1801,1802,1804],{},[588,1803,590],{},[585,1805,1806,1808],{},[588,1807,605],{},[588,1809,598],{},[610,1811,1812],{"encoding":612},"f_{xy} = f_{yx}",[569,1814,1816,1877],{"className":1815,"ariaHidden":601},[617],[569,1817,1819,1822,1868,1871,1874],{"className":1818},[621],[569,1820],{"className":1821,"style":1643},[625],[569,1823,1825,1828],{"className":1824},[630],[569,1826,590],{"className":1827,"style":632},[630,631],[569,1829,1831],{"className":1830},[1046],[569,1832,1834,1860],{"className":1833},[718,719],[569,1835,1837,1857],{"className":1836},[723],[569,1838,1840],{"className":1839,"style":1056},[727],[569,1841,1842,1845],{"style":1059},[569,1843],{"className":1844,"style":1063},[735],[569,1846,1848],{"className":1847},[740,741,742,743],[569,1849,1851,1854],{"className":1850},[630,743],[569,1852,598],{"className":1853},[630,631,743],[569,1855,605],{"className":1856,"style":652},[630,631,743],[569,1858,787],{"className":1859},[786],[569,1861,1863],{"className":1862},[723],[569,1864,1866],{"className":1865,"style":1688},[727],[569,1867],{},[569,1869],{"className":1870,"style":1470},[647],[569,1872,1445],{"className":1873},[1474],[569,1875],{"className":1876,"style":1470},[647],[569,1878,1880,1883],{"className":1879},[621],[569,1881],{"className":1882,"style":1643},[625],[569,1884,1886,1889],{"className":1885},[630],[569,1887,590],{"className":1888,"style":632},[630,631],[569,1890,1892],{"className":1891},[1046],[569,1893,1895,1921],{"className":1894},[718,719],[569,1896,1898,1918],{"className":1897},[723],[569,1899,1901],{"className":1900,"style":1056},[727],[569,1902,1903,1906],{"style":1059},[569,1904],{"className":1905,"style":1063},[735],[569,1907,1909],{"className":1908},[740,741,742,743],[569,1910,1912,1915],{"className":1911},[630,743],[569,1913,605],{"className":1914,"style":652},[630,631,743],[569,1916,598],{"className":1917},[630,631,743],[569,1919,787],{"className":1920},[786],[569,1922,1924],{"className":1923},[723],[569,1925,1927],{"className":1926,"style":1688},[727],[569,1928],{},", wenn die zweiten partiellen Ableitungen stetig sind. Für Funktionen von ",[569,1931,1933,1947],{"className":1932},[572],[569,1934,1936],{"className":1935},[576],[578,1937,1938],{"xmlns":580},[582,1939,1940,1945],{},[585,1941,1942],{},[588,1943,1944],{},"n",[610,1946,1944],{"encoding":612},[569,1948,1950],{"className":1949,"ariaHidden":601},[617],[569,1951,1953,1956],{"className":1952},[621],[569,1954],{"className":1955,"style":856},[625],[569,1957,1944],{"className":1958},[630,631]," Variablen gilt alles entsprechend.",[560,1961,1963],{"id":1962},"beispiele","Beispiele",[565,1965,1966,1967,2152,2153,2181,2182,2210],{},"Für ",[569,1968,1970,2020],{"className":1969},[572],[569,1971,1973],{"className":1972},[576],[578,1974,1975],{"xmlns":580},[582,1976,1977,2017],{},[585,1978,1979,1981,1983,1985,1987,1989,1991,1993,2001,2003,2006,2009,2011],{},[588,1980,590],{},[592,1982,595],{"stretchy":594},[588,1984,598],{},[592,1986,602],{"separator":601},[588,1988,605],{},[592,1990,608],{"stretchy":594},[592,1992,1445],{},[1994,1995,1996,1998],"msup",{},[588,1997,598],{},[1178,1999,2000],{},"2",[588,2002,605],{},[592,2004,2005],{},"+",[1178,2007,2008],{},"3",[588,2010,598],{},[1994,2012,2013,2015],{},[588,2014,605],{},[1178,2016,2008],{},[610,2018,2019],{"encoding":612},"f(x, y) = x^2 y + 3xy^3",[569,2021,2023,2059,2111],{"className":2022,"ariaHidden":601},[617],[569,2024,2026,2029,2032,2035,2038,2041,2044,2047,2050,2053,2056],{"className":2025},[621],[569,2027],{"className":2028,"style":626},[625],[569,2030,590],{"className":2031,"style":632},[630,631],[569,2033,595],{"className":2034},[636],[569,2036,598],{"className":2037},[630,631],[569,2039,602],{"className":2040},[643],[569,2042],{"className":2043,"style":648},[647],[569,2045,605],{"className":2046,"style":652},[630,631],[569,2048,608],{"className":2049},[656],[569,2051],{"className":2052,"style":1470},[647],[569,2054,1445],{"className":2055},[1474],[569,2057],{"className":2058,"style":1470},[647],[569,2060,2062,2066,2097,2100,2104,2108],{"className":2061},[621],[569,2063],{"className":2064,"style":2065},[625],"height:1.0085em;vertical-align:-0.1944em;",[569,2067,2069,2072],{"className":2068},[630],[569,2070,598],{"className":2071},[630,631],[569,2073,2075],{"className":2074},[1046],[569,2076,2078],{"className":2077},[718],[569,2079,2081],{"className":2080},[723],[569,2082,2085],{"className":2083,"style":2084},[727],"height:0.8141em;",[569,2086,2088,2091],{"style":2087},"top:-3.063em;margin-right:0.05em;",[569,2089],{"className":2090,"style":1063},[735],[569,2092,2094],{"className":2093},[740,741,742,743],[569,2095,2000],{"className":2096},[630,743],[569,2098,605],{"className":2099,"style":652},[630,631],[569,2101],{"className":2102,"style":2103},[647],"margin-right:0.2222em;",[569,2105,2005],{"className":2106},[2107],"mbin",[569,2109],{"className":2110,"style":2103},[647],[569,2112,2114,2117,2120,2123],{"className":2113},[621],[569,2115],{"className":2116,"style":2065},[625],[569,2118,2008],{"className":2119},[630],[569,2121,598],{"className":2122},[630,631],[569,2124,2126,2129],{"className":2125},[630],[569,2127,605],{"className":2128,"style":652},[630,631],[569,2130,2132],{"className":2131},[1046],[569,2133,2135],{"className":2134},[718],[569,2136,2138],{"className":2137},[723],[569,2139,2141],{"className":2140,"style":2084},[727],[569,2142,2143,2146],{"style":2087},[569,2144],{"className":2145,"style":1063},[735],[569,2147,2149],{"className":2148},[740,741,742,743],[569,2150,2008],{"className":2151},[630,743]," wird beim Ableiten nach ",[569,2154,2156,2169],{"className":2155},[572],[569,2157,2159],{"className":2158},[576],[578,2160,2161],{"xmlns":580},[582,2162,2163,2167],{},[585,2164,2165],{},[588,2166,598],{},[610,2168,598],{"encoding":612},[569,2170,2172],{"className":2171,"ariaHidden":601},[617],[569,2173,2175,2178],{"className":2174},[621],[569,2176],{"className":2177,"style":856},[625],[569,2179,598],{"className":2180},[630,631]," der Faktor ",[569,2183,2185,2198],{"className":2184},[572],[569,2186,2188],{"className":2187},[576],[578,2189,2190],{"xmlns":580},[582,2191,2192,2196],{},[585,2193,2194],{},[588,2195,605],{},[610,2197,605],{"encoding":612},[569,2199,2201],{"className":2200,"ariaHidden":601},[617],[569,2202,2204,2207],{"className":2203},[621],[569,2205],{"className":2206,"style":826},[625],[569,2208,605],{"className":2209,"style":652},[630,631]," wie eine Konstante behandelt:",[569,2212,2215],{"className":2213},[2214],"katex-display",[569,2216,2218,2287],{"className":2217},[572],[569,2219,2221],{"className":2220},[576],[578,2222,2224],{"xmlns":580,"display":2223},"block",[582,2225,2226,2284],{},[585,2227,2228,2234,2236,2238,2240,2242,2244,2246,2252,2254,2257,2263,2265,2271,2273,2276,2278],{},[1018,2229,2230,2232],{},[588,2231,590],{},[588,2233,598],{},[592,2235,1445],{},[1178,2237,2000],{},[588,2239,598],{},[588,2241,605],{},[592,2243,2005],{},[1178,2245,2008],{},[1994,2247,2248,2250],{},[588,2249,605],{},[1178,2251,2008],{},[592,2253,602],{"separator":601},[647,2255],{"width":2256},"2em",[1018,2258,2259,2261],{},[588,2260,590],{},[588,2262,605],{},[592,2264,1445],{},[1994,2266,2267,2269],{},[588,2268,598],{},[1178,2270,2000],{},[592,2272,2005],{},[1178,2274,2275],{},"9",[588,2277,598],{},[1994,2279,2280,2282],{},[588,2281,605],{},[1178,2283,2000],{},[610,2285,2286],{"encoding":612},"f_x = 2xy + 3y^3, \\qquad f_y = x^2 + 9xy^2",[569,2288,2290,2345,2370,2470,2515],{"className":2289,"ariaHidden":601},[617],[569,2291,2293,2296,2336,2339,2342],{"className":2292},[621],[569,2294],{"className":2295,"style":1036},[625],[569,2297,2299,2302],{"className":2298},[630],[569,2300,590],{"className":2301,"style":632},[630,631],[569,2303,2305],{"className":2304},[1046],[569,2306,2308,2328],{"className":2307},[718,719],[569,2309,2311,2325],{"className":2310},[723],[569,2312,2314],{"className":2313,"style":1056},[727],[569,2315,2316,2319],{"style":1059},[569,2317],{"className":2318,"style":1063},[735],[569,2320,2322],{"className":2321},[740,741,742,743],[569,2323,598],{"className":2324},[630,631,743],[569,2326,787],{"className":2327},[786],[569,2329,2331],{"className":2330},[723],[569,2332,2334],{"className":2333,"style":1079},[727],[569,2335],{},[569,2337],{"className":2338,"style":1470},[647],[569,2340,1445],{"className":2341},[1474],[569,2343],{"className":2344,"style":1470},[647],[569,2346,2348,2352,2355,2358,2361,2364,2367],{"className":2347},[621],[569,2349],{"className":2350,"style":2351},[625],"height:0.8389em;vertical-align:-0.1944em;",[569,2353,2000],{"className":2354},[630],[569,2356,598],{"className":2357},[630,631],[569,2359,605],{"className":2360,"style":652},[630,631],[569,2362],{"className":2363,"style":2103},[647],[569,2365,2005],{"className":2366},[2107],[569,2368],{"className":2369,"style":2103},[647],[569,2371,2373,2377,2380,2411,2414,2418,2421,2461,2464,2467],{"className":2372},[621],[569,2374],{"className":2375,"style":2376},[625],"height:1.1502em;vertical-align:-0.2861em;",[569,2378,2008],{"className":2379},[630],[569,2381,2383,2386],{"className":2382},[630],[569,2384,605],{"className":2385,"style":652},[630,631],[569,2387,2389],{"className":2388},[1046],[569,2390,2392],{"className":2391},[718],[569,2393,2395],{"className":2394},[723],[569,2396,2399],{"className":2397,"style":2398},[727],"height:0.8641em;",[569,2400,2402,2405],{"style":2401},"top:-3.113em;margin-right:0.05em;",[569,2403],{"className":2404,"style":1063},[735],[569,2406,2408],{"className":2407},[740,741,742,743],[569,2409,2008],{"className":2410},[630,743],[569,2412,602],{"className":2413},[643],[569,2415],{"className":2416,"style":2417},[647],"margin-right:2em;",[569,2419],{"className":2420,"style":648},[647],[569,2422,2424,2427],{"className":2423},[630],[569,2425,590],{"className":2426,"style":632},[630,631],[569,2428,2430],{"className":2429},[1046],[569,2431,2433,2453],{"className":2432},[718,719],[569,2434,2436,2450],{"className":2435},[723],[569,2437,2439],{"className":2438,"style":1056},[727],[569,2440,2441,2444],{"style":1059},[569,2442],{"className":2443,"style":1063},[735],[569,2445,2447],{"className":2446},[740,741,742,743],[569,2448,605],{"className":2449,"style":652},[630,631,743],[569,2451,787],{"className":2452},[786],[569,2454,2456],{"className":2455},[723],[569,2457,2459],{"className":2458,"style":1688},[727],[569,2460],{},[569,2462],{"className":2463,"style":1470},[647],[569,2465,1445],{"className":2466},[1474],[569,2468],{"className":2469,"style":1470},[647],[569,2471,2473,2477,2506,2509,2512],{"className":2472},[621],[569,2474],{"className":2475,"style":2476},[625],"height:0.9474em;vertical-align:-0.0833em;",[569,2478,2480,2483],{"className":2479},[630],[569,2481,598],{"className":2482},[630,631],[569,2484,2486],{"className":2485},[1046],[569,2487,2489],{"className":2488},[718],[569,2490,2492],{"className":2491},[723],[569,2493,2495],{"className":2494,"style":2398},[727],[569,2496,2497,2500],{"style":2401},[569,2498],{"className":2499,"style":1063},[735],[569,2501,2503],{"className":2502},[740,741,742,743],[569,2504,2000],{"className":2505},[630,743],[569,2507],{"className":2508,"style":2103},[647],[569,2510,2005],{"className":2511},[2107],[569,2513],{"className":2514,"style":2103},[647],[569,2516,2518,2522,2525,2528],{"className":2517},[621],[569,2519],{"className":2520,"style":2521},[625],"height:1.0585em;vertical-align:-0.1944em;",[569,2523,2275],{"className":2524},[630],[569,2526,598],{"className":2527},[630,631],[569,2529,2531,2534],{"className":2530},[630],[569,2532,605],{"className":2533,"style":652},[630,631],[569,2535,2537],{"className":2536},[1046],[569,2538,2540],{"className":2539},[718],[569,2541,2543],{"className":2542},[723],[569,2544,2546],{"className":2545,"style":2398},[727],[569,2547,2548,2551],{"style":2401},[569,2549],{"className":2550,"style":1063},[735],[569,2552,2554],{"className":2553},[740,741,742,743],[569,2555,2000],{"className":2556},[630,743],[565,2558,2559,2560,2612,2613,1691,2782,2949,2950,1241],{},"An der Stelle ",[569,2561,2563,2585],{"className":2562},[572],[569,2564,2566],{"className":2565},[576],[578,2567,2568],{"xmlns":580},[582,2569,2570,2582],{},[585,2571,2572,2574,2576,2578,2580],{},[592,2573,595],{"stretchy":594},[1178,2575,1180],{},[592,2577,602],{"separator":601},[1178,2579,2000],{},[592,2581,608],{"stretchy":594},[610,2583,2584],{"encoding":612},"(1, 2)",[569,2586,2588],{"className":2587,"ariaHidden":601},[617],[569,2589,2591,2594,2597,2600,2603,2606,2609],{"className":2590},[621],[569,2592],{"className":2593,"style":626},[625],[569,2595,595],{"className":2596},[636],[569,2598,1180],{"className":2599},[630],[569,2601,602],{"className":2602},[643],[569,2604],{"className":2605,"style":648},[647],[569,2607,2000],{"className":2608},[630],[569,2610,608],{"className":2611},[656]," ist ",[569,2614,2616,2659],{"className":2615},[572],[569,2617,2619],{"className":2618},[576],[578,2620,2621],{"xmlns":580},[582,2622,2623,2656],{},[585,2624,2625,2631,2633,2635,2637,2639,2641,2643,2646,2648,2651,2653],{},[1018,2626,2627,2629],{},[588,2628,590],{},[588,2630,598],{},[592,2632,595],{"stretchy":594},[1178,2634,1180],{},[592,2636,602],{"separator":601},[1178,2638,2000],{},[592,2640,608],{"stretchy":594},[592,2642,1445],{},[1178,2644,2645],{},"4",[592,2647,2005],{},[1178,2649,2650],{},"24",[592,2652,1445],{},[1178,2654,2655],{},"28",[610,2657,2658],{"encoding":612},"f_x(1, 2) = 4 + 24 = 28",[569,2660,2662,2735,2754,2773],{"className":2661,"ariaHidden":601},[617],[569,2663,2665,2668,2708,2711,2714,2717,2720,2723,2726,2729,2732],{"className":2664},[621],[569,2666],{"className":2667,"style":626},[625],[569,2669,2671,2674],{"className":2670},[630],[569,2672,590],{"className":2673,"style":632},[630,631],[569,2675,2677],{"className":2676},[1046],[569,2678,2680,2700],{"className":2679},[718,719],[569,2681,2683,2697],{"className":2682},[723],[569,2684,2686],{"className":2685,"style":1056},[727],[569,2687,2688,2691],{"style":1059},[569,2689],{"className":2690,"style":1063},[735],[569,2692,2694],{"className":2693},[740,741,742,743],[569,2695,598],{"className":2696},[630,631,743],[569,2698,787],{"className":2699},[786],[569,2701,2703],{"className":2702},[723],[569,2704,2706],{"className":2705,"style":1079},[727],[569,2707],{},[569,2709,595],{"className":2710},[636],[569,2712,1180],{"className":2713},[630],[569,2715,602],{"className":2716},[643],[569,2718],{"className":2719,"style":648},[647],[569,2721,2000],{"className":2722},[630],[569,2724,608],{"className":2725},[656],[569,2727],{"className":2728,"style":1470},[647],[569,2730,1445],{"className":2731},[1474],[569,2733],{"className":2734,"style":1470},[647],[569,2736,2738,2742,2745,2748,2751],{"className":2737},[621],[569,2739],{"className":2740,"style":2741},[625],"height:0.7278em;vertical-align:-0.0833em;",[569,2743,2645],{"className":2744},[630],[569,2746],{"className":2747,"style":2103},[647],[569,2749,2005],{"className":2750},[2107],[569,2752],{"className":2753,"style":2103},[647],[569,2755,2757,2761,2764,2767,2770],{"className":2756},[621],[569,2758],{"className":2759,"style":2760},[625],"height:0.6444em;",[569,2762,2650],{"className":2763},[630],[569,2765],{"className":2766,"style":1470},[647],[569,2768,1445],{"className":2769},[1474],[569,2771],{"className":2772,"style":1470},[647],[569,2774,2776,2779],{"className":2775},[621],[569,2777],{"className":2778,"style":2760},[625],[569,2780,2655],{"className":2781},[630],[569,2783,2785,2827],{"className":2784},[572],[569,2786,2788],{"className":2787},[576],[578,2789,2790],{"xmlns":580},[582,2791,2792,2824],{},[585,2793,2794,2800,2802,2804,2806,2808,2810,2812,2814,2816,2819,2821],{},[1018,2795,2796,2798],{},[588,2797,590],{},[588,2799,605],{},[592,2801,595],{"stretchy":594},[1178,2803,1180],{},[592,2805,602],{"separator":601},[1178,2807,2000],{},[592,2809,608],{"stretchy":594},[592,2811,1445],{},[1178,2813,1180],{},[592,2815,2005],{},[1178,2817,2818],{},"36",[592,2820,1445],{},[1178,2822,2823],{},"37",[610,2825,2826],{"encoding":612},"f_y(1, 2) = 1 + 36 = 37",[569,2828,2830,2904,2922,2940],{"className":2829,"ariaHidden":601},[617],[569,2831,2833,2837,2877,2880,2883,2886,2889,2892,2895,2898,2901],{"className":2832},[621],[569,2834],{"className":2835,"style":2836},[625],"height:1.0361em;vertical-align:-0.2861em;",[569,2838,2840,2843],{"className":2839},[630],[569,2841,590],{"className":2842,"style":632},[630,631],[569,2844,2846],{"className":2845},[1046],[569,2847,2849,2869],{"className":2848},[718,719],[569,2850,2852,2866],{"className":2851},[723],[569,2853,2855],{"className":2854,"style":1056},[727],[569,2856,2857,2860],{"style":1059},[569,2858],{"className":2859,"style":1063},[735],[569,2861,2863],{"className":2862},[740,741,742,743],[569,2864,605],{"className":2865,"style":652},[630,631,743],[569,2867,787],{"className":2868},[786],[569,2870,2872],{"className":2871},[723],[569,2873,2875],{"className":2874,"style":1688},[727],[569,2876],{},[569,2878,595],{"className":2879},[636],[569,2881,1180],{"className":2882},[630],[569,2884,602],{"className":2885},[643],[569,2887],{"className":2888,"style":648},[647],[569,2890,2000],{"className":2891},[630],[569,2893,608],{"className":2894},[656],[569,2896],{"className":2897,"style":1470},[647],[569,2899,1445],{"className":2900},[1474],[569,2902],{"className":2903,"style":1470},[647],[569,2905,2907,2910,2913,2916,2919],{"className":2906},[621],[569,2908],{"className":2909,"style":2741},[625],[569,2911,1180],{"className":2912},[630],[569,2914],{"className":2915,"style":2103},[647],[569,2917,2005],{"className":2918},[2107],[569,2920],{"className":2921,"style":2103},[647],[569,2923,2925,2928,2931,2934,2937],{"className":2924},[621],[569,2926],{"className":2927,"style":2760},[625],[569,2929,2818],{"className":2930},[630],[569,2932],{"className":2933,"style":1470},[647],[569,2935,1445],{"className":2936},[1474],[569,2938],{"className":2939,"style":1470},[647],[569,2941,2943,2946],{"className":2942},[621],[569,2944],{"className":2945,"style":2760},[625],[569,2947,2823],{"className":2948},[630],". Die gemischten Ableitungen stimmen überein: ",[569,2951,2953,3003],{"className":2952},[572],[569,2954,2956],{"className":2955},[576],[578,2957,2958],{"xmlns":580},[582,2959,2960,3000],{},[585,2961,2962,2972,2974,2984,2986,2988,2990,2992,2994],{},[1018,2963,2964,2966],{},[588,2965,590],{},[585,2967,2968,2970],{},[588,2969,598],{},[588,2971,605],{},[592,2973,1445],{},[1018,2975,2976,2978],{},[588,2977,590],{},[585,2979,2980,2982],{},[588,2981,605],{},[588,2983,598],{},[592,2985,1445],{},[1178,2987,2000],{},[588,2989,598],{},[592,2991,2005],{},[1178,2993,2275],{},[1994,2995,2996,2998],{},[588,2997,605],{},[1178,2999,2000],{},[610,3001,3002],{"encoding":612},"f_{xy} = f_{yx} = 2x + 9y^2",[569,3004,3006,3067,3128,3149],{"className":3005,"ariaHidden":601},[617],[569,3007,3009,3012,3058,3061,3064],{"className":3008},[621],[569,3010],{"className":3011,"style":1643},[625],[569,3013,3015,3018],{"className":3014},[630],[569,3016,590],{"className":3017,"style":632},[630,631],[569,3019,3021],{"className":3020},[1046],[569,3022,3024,3050],{"className":3023},[718,719],[569,3025,3027,3047],{"className":3026},[723],[569,3028,3030],{"className":3029,"style":1056},[727],[569,3031,3032,3035],{"style":1059},[569,3033],{"className":3034,"style":1063},[735],[569,3036,3038],{"className":3037},[740,741,742,743],[569,3039,3041,3044],{"className":3040},[630,743],[569,3042,598],{"className":3043},[630,631,743],[569,3045,605],{"className":3046,"style":652},[630,631,743],[569,3048,787],{"className":3049},[786],[569,3051,3053],{"className":3052},[723],[569,3054,3056],{"className":3055,"style":1688},[727],[569,3057],{},[569,3059],{"className":3060,"style":1470},[647],[569,3062,1445],{"className":3063},[1474],[569,3065],{"className":3066,"style":1470},[647],[569,3068,3070,3073,3119,3122,3125],{"className":3069},[621],[569,3071],{"className":3072,"style":1643},[625],[569,3074,3076,3079],{"className":3075},[630],[569,3077,590],{"className":3078,"style":632},[630,631],[569,3080,3082],{"className":3081},[1046],[569,3083,3085,3111],{"className":3084},[718,719],[569,3086,3088,3108],{"className":3087},[723],[569,3089,3091],{"className":3090,"style":1056},[727],[569,3092,3093,3096],{"style":1059},[569,3094],{"className":3095,"style":1063},[735],[569,3097,3099],{"className":3098},[740,741,742,743],[569,3100,3102,3105],{"className":3101},[630,743],[569,3103,605],{"className":3104,"style":652},[630,631,743],[569,3106,598],{"className":3107},[630,631,743],[569,3109,787],{"className":3110},[786],[569,3112,3114],{"className":3113},[723],[569,3115,3117],{"className":3116,"style":1688},[727],[569,3118],{},[569,3120],{"className":3121,"style":1470},[647],[569,3123,1445],{"className":3124},[1474],[569,3126],{"className":3127,"style":1470},[647],[569,3129,3131,3134,3137,3140,3143,3146],{"className":3130},[621],[569,3132],{"className":3133,"style":2741},[625],[569,3135,2000],{"className":3136},[630],[569,3138,598],{"className":3139},[630,631],[569,3141],{"className":3142,"style":2103},[647],[569,3144,2005],{"className":3145},[2107],[569,3147],{"className":3148,"style":2103},[647],[569,3150,3152,3155,3158],{"className":3151},[621],[569,3153],{"className":3154,"style":2065},[625],[569,3156,2275],{"className":3157},[630],[569,3159,3161,3164],{"className":3160},[630],[569,3162,605],{"className":3163,"style":652},[630,631],[569,3165,3167],{"className":3166},[1046],[569,3168,3170],{"className":3169},[718],[569,3171,3173],{"className":3172},[723],[569,3174,3176],{"className":3175,"style":2084},[727],[569,3177,3178,3181],{"style":2087},[569,3179],{"className":3180,"style":1063},[735],[569,3182,3184],{"className":3183},[740,741,742,743],[569,3185,2000],{"className":3186},[630,743],[565,3188,1966,3189,3293,3294,3417,3418,2612,3470,1241],{},[569,3190,3192,3232],{"className":3191},[572],[569,3193,3195],{"className":3194},[576],[578,3196,3197],{"xmlns":580},[582,3198,3199,3229],{},[585,3200,3201,3203,3205,3207,3209,3211,3213,3215,3218,3221,3223,3225,3227],{},[588,3202,590],{},[592,3204,595],{"stretchy":594},[588,3206,598],{},[592,3208,602],{"separator":601},[588,3210,605],{},[592,3212,608],{"stretchy":594},[592,3214,1445],{},[588,3216,3217],{},"sin",[592,3219,3220],{},"⁡",[592,3222,595],{"stretchy":594},[588,3224,598],{},[588,3226,605],{},[592,3228,608],{"stretchy":594},[610,3230,3231],{"encoding":612},"f(x, y) = \\sin(xy)",[569,3233,3235,3271],{"className":3234,"ariaHidden":601},[617],[569,3236,3238,3241,3244,3247,3250,3253,3256,3259,3262,3265,3268],{"className":3237},[621],[569,3239],{"className":3240,"style":626},[625],[569,3242,590],{"className":3243,"style":632},[630,631],[569,3245,595],{"className":3246},[636],[569,3248,598],{"className":3249},[630,631],[569,3251,602],{"className":3252},[643],[569,3254],{"className":3255,"style":648},[647],[569,3257,605],{"className":3258,"style":652},[630,631],[569,3260,608],{"className":3261},[656],[569,3263],{"className":3264,"style":1470},[647],[569,3266,1445],{"className":3267},[1474],[569,3269],{"className":3270,"style":1470},[647],[569,3272,3274,3277,3281,3284,3287,3290],{"className":3273},[621],[569,3275],{"className":3276,"style":626},[625],[569,3278,3217],{"className":3279},[3280],"mop",[569,3282,595],{"className":3283},[636],[569,3285,598],{"className":3286},[630,631],[569,3288,605],{"className":3289,"style":652},[630,631],[569,3291,608],{"className":3292},[656]," liefert die Kettenregel ",[569,3295,3297,3332],{"className":3296},[572],[569,3298,3300],{"className":3299},[576],[578,3301,3302],{"xmlns":580},[582,3303,3304,3329],{},[585,3305,3306,3312,3314,3316,3319,3321,3323,3325,3327],{},[1018,3307,3308,3310],{},[588,3309,590],{},[588,3311,598],{},[592,3313,1445],{},[588,3315,605],{},[588,3317,3318],{},"cos",[592,3320,3220],{},[592,3322,595],{"stretchy":594},[588,3324,598],{},[588,3326,605],{},[592,3328,608],{"stretchy":594},[610,3330,3331],{"encoding":612},"f_x = y \\cos(xy)",[569,3333,3335,3390],{"className":3334,"ariaHidden":601},[617],[569,3336,3338,3341,3381,3384,3387],{"className":3337},[621],[569,3339],{"className":3340,"style":1036},[625],[569,3342,3344,3347],{"className":3343},[630],[569,3345,590],{"className":3346,"style":632},[630,631],[569,3348,3350],{"className":3349},[1046],[569,3351,3353,3373],{"className":3352},[718,719],[569,3354,3356,3370],{"className":3355},[723],[569,3357,3359],{"className":3358,"style":1056},[727],[569,3360,3361,3364],{"style":1059},[569,3362],{"className":3363,"style":1063},[735],[569,3365,3367],{"className":3366},[740,741,742,743],[569,3368,598],{"className":3369},[630,631,743],[569,3371,787],{"className":3372},[786],[569,3374,3376],{"className":3375},[723],[569,3377,3379],{"className":3378,"style":1079},[727],[569,3380],{},[569,3382],{"className":3383,"style":1470},[647],[569,3385,1445],{"className":3386},[1474],[569,3388],{"className":3389,"style":1470},[647],[569,3391,3393,3396,3399,3402,3405,3408,3411,3414],{"className":3392},[621],[569,3394],{"className":3395,"style":626},[625],[569,3397,605],{"className":3398,"style":652},[630,631],[569,3400],{"className":3401,"style":648},[647],[569,3403,3318],{"className":3404},[3280],[569,3406,595],{"className":3407},[636],[569,3409,598],{"className":3410},[630,631],[569,3412,605],{"className":3413,"style":652},[630,631],[569,3415,608],{"className":3416},[656],". An der Stelle ",[569,3419,3421,3443],{"className":3420},[572],[569,3422,3424],{"className":3423},[576],[578,3425,3426],{"xmlns":580},[582,3427,3428,3440],{},[585,3429,3430,3432,3434,3436,3438],{},[592,3431,595],{"stretchy":594},[1178,3433,1271],{},[592,3435,602],{"separator":601},[1178,3437,2000],{},[592,3439,608],{"stretchy":594},[610,3441,3442],{"encoding":612},"(0, 2)",[569,3444,3446],{"className":3445,"ariaHidden":601},[617],[569,3447,3449,3452,3455,3458,3461,3464,3467],{"className":3448},[621],[569,3450],{"className":3451,"style":626},[625],[569,3453,595],{"className":3454},[636],[569,3456,1271],{"className":3457},[630],[569,3459,602],{"className":3460},[643],[569,3462],{"className":3463,"style":648},[647],[569,3465,2000],{"className":3466},[630],[569,3468,608],{"className":3469},[656],[569,3471,3473,3515],{"className":3472},[572],[569,3474,3476],{"className":3475},[576],[578,3477,3478],{"xmlns":580},[582,3479,3480,3512],{},[585,3481,3482,3488,3490,3492,3494,3496,3498,3500,3502,3504,3506,3508,3510],{},[1018,3483,3484,3486],{},[588,3485,590],{},[588,3487,598],{},[592,3489,595],{"stretchy":594},[1178,3491,1271],{},[592,3493,602],{"separator":601},[1178,3495,2000],{},[592,3497,608],{"stretchy":594},[592,3499,1445],{},[1178,3501,2000],{},[588,3503,3318],{},[592,3505,3220],{},[1178,3507,1271],{},[592,3509,1445],{},[1178,3511,2000],{},[610,3513,3514],{"encoding":612},"f_x(0, 2) = 2 \\cos 0 = 2",[569,3516,3518,3591,3621],{"className":3517,"ariaHidden":601},[617],[569,3519,3521,3524,3564,3567,3570,3573,3576,3579,3582,3585,3588],{"className":3520},[621],[569,3522],{"className":3523,"style":626},[625],[569,3525,3527,3530],{"className":3526},[630],[569,3528,590],{"className":3529,"style":632},[630,631],[569,3531,3533],{"className":3532},[1046],[569,3534,3536,3556],{"className":3535},[718,719],[569,3537,3539,3553],{"className":3538},[723],[569,3540,3542],{"className":3541,"style":1056},[727],[569,3543,3544,3547],{"style":1059},[569,3545],{"className":3546,"style":1063},[735],[569,3548,3550],{"className":3549},[740,741,742,743],[569,3551,598],{"className":3552},[630,631,743],[569,3554,787],{"className":3555},[786],[569,3557,3559],{"className":3558},[723],[569,3560,3562],{"className":3561,"style":1079},[727],[569,3563],{},[569,3565,595],{"className":3566},[636],[569,3568,1271],{"className":3569},[630],[569,3571,602],{"className":3572},[643],[569,3574],{"className":3575,"style":648},[647],[569,3577,2000],{"className":3578},[630],[569,3580,608],{"className":3581},[656],[569,3583],{"className":3584,"style":1470},[647],[569,3586,1445],{"className":3587},[1474],[569,3589],{"className":3590,"style":1470},[647],[569,3592,3594,3597,3600,3603,3606,3609,3612,3615,3618],{"className":3593},[621],[569,3595],{"className":3596,"style":2760},[625],[569,3598,2000],{"className":3599},[630],[569,3601],{"className":3602,"style":648},[647],[569,3604,3318],{"className":3605},[3280],[569,3607],{"className":3608,"style":648},[647],[569,3610,1271],{"className":3611},[630],[569,3613],{"className":3614,"style":1470},[647],[569,3616,1445],{"className":3617},[1474],[569,3619],{"className":3620,"style":1470},[647],[569,3622,3624,3627],{"className":3623},[621],[569,3625],{"className":3626,"style":2760},[625],[569,3628,2000],{"className":3629},[630],[560,3631,3633],{"id":3632},"typische-fehler","Typische Fehler",[3635,3636,3637,3960,4216],"ul",{},[3638,3639,3640,3641,3799,3800,3828,3829,3868,3869,1241],"li",{},"Die festgehaltene Variable mit ableiten. Bei ",[569,3642,3644,3678],{"className":3643},[572],[569,3645,3647],{"className":3646},[576],[578,3648,3649],{"xmlns":580},[582,3650,3651,3675],{},[585,3652,3653,3663,3665,3671,3673],{},[676,3654,3655,3657],{},[588,3656,683],{"mathvariant":682},[585,3658,3659,3661],{},[588,3660,683],{"mathvariant":682},[588,3662,598],{},[592,3664,595],{"stretchy":594},[1994,3666,3667,3669],{},[588,3668,598],{},[1178,3670,2000],{},[588,3672,605],{},[592,3674,608],{"stretchy":594},[610,3676,3677],{"encoding":612},"\\frac{\\partial}{\\partial x}(x^2 y)",[569,3679,3681],{"className":3680,"ariaHidden":601},[617],[569,3682,3684,3688,3761,3764,3793,3796],{"className":3683},[621],[569,3685],{"className":3686,"style":3687},[625],"height:1.2251em;vertical-align:-0.345em;",[569,3689,3691,3694,3758],{"className":3690},[630],[569,3692],{"className":3693},[636,711],[569,3695,3697],{"className":3696},[676],[569,3698,3700,3750],{"className":3699},[718,719],[569,3701,3703,3747],{"className":3702},[723],[569,3704,3707,3724,3732],{"className":3705,"style":3706},[727],"height:0.8801em;",[569,3708,3709,3712],{"style":731},[569,3710],{"className":3711,"style":736},[735],[569,3713,3715],{"className":3714},[740,741,742,743],[569,3716,3718,3721],{"className":3717},[630,743],[569,3719,683],{"className":3720,"style":750},[630,743],[569,3722,598],{"className":3723},[630,631,743],[569,3725,3726,3729],{"style":756},[569,3727],{"className":3728,"style":736},[735],[569,3730],{"className":3731,"style":764},[763],[569,3733,3735,3738],{"style":3734},"top:-3.394em;",[569,3736],{"className":3737,"style":736},[735],[569,3739,3741],{"className":3740},[740,741,742,743],[569,3742,3744],{"className":3743},[630,743],[569,3745,683],{"className":3746,"style":750},[630,743],[569,3748,787],{"className":3749},[786],[569,3751,3753],{"className":3752},[723],[569,3754,3756],{"className":3755,"style":794},[727],[569,3757],{},[569,3759],{"className":3760},[656,711],[569,3762,595],{"className":3763},[636],[569,3765,3767,3770],{"className":3766},[630],[569,3768,598],{"className":3769},[630,631],[569,3771,3773],{"className":3772},[1046],[569,3774,3776],{"className":3775},[718],[569,3777,3779],{"className":3778},[723],[569,3780,3782],{"className":3781,"style":2084},[727],[569,3783,3784,3787],{"style":2087},[569,3785],{"className":3786,"style":1063},[735],[569,3788,3790],{"className":3789},[740,741,742,743],[569,3791,2000],{"className":3792},[630,743],[569,3794,605],{"className":3795,"style":652},[630,631],[569,3797,608],{"className":3798},[656]," bleibt ",[569,3801,3803,3816],{"className":3802},[572],[569,3804,3806],{"className":3805},[576],[578,3807,3808],{"xmlns":580},[582,3809,3810,3814],{},[585,3811,3812],{},[588,3813,605],{},[610,3815,605],{"encoding":612},[569,3817,3819],{"className":3818,"ariaHidden":601},[617],[569,3820,3822,3825],{"className":3821},[621],[569,3823],{"className":3824,"style":826},[625],[569,3826,605],{"className":3827,"style":652},[630,631]," als Faktor stehen: ",[569,3830,3832,3850],{"className":3831},[572],[569,3833,3835],{"className":3834},[576],[578,3836,3837],{"xmlns":580},[582,3838,3839,3847],{},[585,3840,3841,3843,3845],{},[1178,3842,2000],{},[588,3844,598],{},[588,3846,605],{},[610,3848,3849],{"encoding":612},"2xy",[569,3851,3853],{"className":3852,"ariaHidden":601},[617],[569,3854,3856,3859,3862,3865],{"className":3855},[621],[569,3857],{"className":3858,"style":2351},[625],[569,3860,2000],{"className":3861},[630],[569,3863,598],{"className":3864},[630,631],[569,3866,605],{"className":3867,"style":652},[630,631],", nicht ",[569,3870,3872,3898],{"className":3871},[572],[569,3873,3875],{"className":3874},[576],[578,3876,3877],{"xmlns":580},[582,3878,3879,3895],{},[585,3880,3881,3883,3885,3887,3889],{},[1178,3882,2000],{},[588,3884,598],{},[588,3886,605],{},[592,3888,2005],{},[1994,3890,3891,3893],{},[588,3892,598],{},[1178,3894,2000],{},[610,3896,3897],{"encoding":612},"2xy + x^2",[569,3899,3901,3925],{"className":3900,"ariaHidden":601},[617],[569,3902,3904,3907,3910,3913,3916,3919,3922],{"className":3903},[621],[569,3905],{"className":3906,"style":2351},[625],[569,3908,2000],{"className":3909},[630],[569,3911,598],{"className":3912},[630,631],[569,3914,605],{"className":3915,"style":652},[630,631],[569,3917],{"className":3918,"style":2103},[647],[569,3920,2005],{"className":3921},[2107],[569,3923],{"className":3924,"style":2103},[647],[569,3926,3928,3931],{"className":3927},[621],[569,3929],{"className":3930,"style":2084},[625],[569,3932,3934,3937],{"className":3933},[630],[569,3935,598],{"className":3936},[630,631],[569,3938,3940],{"className":3939},[1046],[569,3941,3943],{"className":3942},[718],[569,3944,3946],{"className":3945},[723],[569,3947,3949],{"className":3948,"style":2084},[727],[569,3950,3951,3954],{"style":2087},[569,3952],{"className":3953,"style":1063},[735],[569,3955,3957],{"className":3956},[740,741,742,743],[569,3958,2000],{"className":3959},[630,743],[3638,3961,3962,3963,3991,3992,4020,4021,1241],{},"Einen Summanden, der nur von ",[569,3964,3966,3979],{"className":3965},[572],[569,3967,3969],{"className":3968},[576],[578,3970,3971],{"xmlns":580},[582,3972,3973,3977],{},[585,3974,3975],{},[588,3976,605],{},[610,3978,605],{"encoding":612},[569,3980,3982],{"className":3981,"ariaHidden":601},[617],[569,3983,3985,3988],{"className":3984},[621],[569,3986],{"className":3987,"style":826},[625],[569,3989,605],{"className":3990,"style":652},[630,631]," abhängt, beim Ableiten nach ",[569,3993,3995,4008],{"className":3994},[572],[569,3996,3998],{"className":3997},[576],[578,3999,4000],{"xmlns":580},[582,4001,4002,4006],{},[585,4003,4004],{},[588,4005,598],{},[610,4007,598],{"encoding":612},[569,4009,4011],{"className":4010,"ariaHidden":601},[617],[569,4012,4014,4017],{"className":4013},[621],[569,4015],{"className":4016,"style":856},[625],[569,4018,598],{"className":4019},[630,631]," stehen lassen. Er fällt weg, z.B. ",[569,4022,4024,4064],{"className":4023},[572],[569,4025,4027],{"className":4026},[576],[578,4028,4029],{"xmlns":580},[582,4030,4031,4061],{},[585,4032,4033,4043,4045,4047,4049,4055,4057,4059],{},[676,4034,4035,4037],{},[588,4036,683],{"mathvariant":682},[585,4038,4039,4041],{},[588,4040,683],{"mathvariant":682},[588,4042,598],{},[592,4044,595],{"stretchy":594},[588,4046,598],{},[592,4048,2005],{},[1994,4050,4051,4053],{},[588,4052,605],{},[1178,4054,2008],{},[592,4056,608],{"stretchy":594},[592,4058,1445],{},[1178,4060,1180],{},[610,4062,4063],{"encoding":612},"\\frac{\\partial}{\\partial x}(x + y^3) = 1",[569,4065,4067,4159,4207],{"className":4066,"ariaHidden":601},[617],[569,4068,4070,4073,4144,4147,4150,4153,4156],{"className":4069},[621],[569,4071],{"className":4072,"style":3687},[625],[569,4074,4076,4079,4141],{"className":4075},[630],[569,4077],{"className":4078},[636,711],[569,4080,4082],{"className":4081},[676],[569,4083,4085,4133],{"className":4084},[718,719],[569,4086,4088,4130],{"className":4087},[723],[569,4089,4091,4108,4116],{"className":4090,"style":3706},[727],[569,4092,4093,4096],{"style":731},[569,4094],{"className":4095,"style":736},[735],[569,4097,4099],{"className":4098},[740,741,742,743],[569,4100,4102,4105],{"className":4101},[630,743],[569,4103,683],{"className":4104,"style":750},[630,743],[569,4106,598],{"className":4107},[630,631,743],[569,4109,4110,4113],{"style":756},[569,4111],{"className":4112,"style":736},[735],[569,4114],{"className":4115,"style":764},[763],[569,4117,4118,4121],{"style":3734},[569,4119],{"className":4120,"style":736},[735],[569,4122,4124],{"className":4123},[740,741,742,743],[569,4125,4127],{"className":4126},[630,743],[569,4128,683],{"className":4129,"style":750},[630,743],[569,4131,787],{"className":4132},[786],[569,4134,4136],{"className":4135},[723],[569,4137,4139],{"className":4138,"style":794},[727],[569,4140],{},[569,4142],{"className":4143},[656,711],[569,4145,595],{"className":4146},[636],[569,4148,598],{"className":4149},[630,631],[569,4151],{"className":4152,"style":2103},[647],[569,4154,2005],{"className":4155},[2107],[569,4157],{"className":4158,"style":2103},[647],[569,4160,4162,4166,4195,4198,4201,4204],{"className":4161},[621],[569,4163],{"className":4164,"style":4165},[625],"height:1.0641em;vertical-align:-0.25em;",[569,4167,4169,4172],{"className":4168},[630],[569,4170,605],{"className":4171,"style":652},[630,631],[569,4173,4175],{"className":4174},[1046],[569,4176,4178],{"className":4177},[718],[569,4179,4181],{"className":4180},[723],[569,4182,4184],{"className":4183,"style":2084},[727],[569,4185,4186,4189],{"style":2087},[569,4187],{"className":4188,"style":1063},[735],[569,4190,4192],{"className":4191},[740,741,742,743],[569,4193,2008],{"className":4194},[630,743],[569,4196,608],{"className":4197},[656],[569,4199],{"className":4200,"style":1470},[647],[569,4202,1445],{"className":4203},[1474],[569,4205],{"className":4206,"style":1470},[647],[569,4208,4210,4213],{"className":4209},[621],[569,4211],{"className":4212,"style":2760},[625],[569,4214,1180],{"className":4215},[630],[3638,4217,4218,4219,4453,4454,4533],{},"Aus der Existenz aller partiellen Ableitungen auf Stetigkeit schließen. Die Funktion ",[569,4220,4222,4272],{"className":4221},[572],[569,4223,4225],{"className":4224},[576],[578,4226,4227],{"xmlns":580},[582,4228,4229,4269],{},[585,4230,4231,4233,4235,4237,4239,4241,4243,4245],{},[588,4232,590],{},[592,4234,595],{"stretchy":594},[588,4236,598],{},[592,4238,602],{"separator":601},[588,4240,605],{},[592,4242,608],{"stretchy":594},[592,4244,1445],{},[676,4246,4247,4253],{},[585,4248,4249,4251],{},[588,4250,598],{},[588,4252,605],{},[585,4254,4255,4261,4263],{},[1994,4256,4257,4259],{},[588,4258,598],{},[1178,4260,2000],{},[592,4262,2005],{},[1994,4264,4265,4267],{},[588,4266,605],{},[1178,4268,2000],{},[610,4270,4271],{"encoding":612},"f(x, y) = \\frac{xy}{x^2 + y^2}",[569,4273,4275,4311],{"className":4274,"ariaHidden":601},[617],[569,4276,4278,4281,4284,4287,4290,4293,4296,4299,4302,4305,4308],{"className":4277},[621],[569,4279],{"className":4280,"style":626},[625],[569,4282,590],{"className":4283,"style":632},[630,631],[569,4285,595],{"className":4286},[636],[569,4288,598],{"className":4289},[630,631],[569,4291,602],{"className":4292},[643],[569,4294],{"className":4295,"style":648},[647],[569,4297,605],{"className":4298,"style":652},[630,631],[569,4300,608],{"className":4301},[656],[569,4303],{"className":4304,"style":1470},[647],[569,4306,1445],{"className":4307},[1474],[569,4309],{"className":4310,"style":1470},[647],[569,4312,4314,4318],{"className":4313},[621],[569,4315],{"className":4316,"style":4317},[625],"height:1.2286em;vertical-align:-0.4811em;",[569,4319,4321,4324,4450],{"className":4320},[630],[569,4322],{"className":4323},[636,711],[569,4325,4327],{"className":4326},[676],[569,4328,4330,4442],{"className":4329},[718,719],[569,4331,4333,4439],{"className":4332},[723],[569,4334,4337,4414,4422],{"className":4335,"style":4336},[727],"height:0.7475em;",[569,4338,4339,4342],{"style":731},[569,4340],{"className":4341,"style":736},[735],[569,4343,4345],{"className":4344},[740,741,742,743],[569,4346,4348,4382,4385],{"className":4347},[630,743],[569,4349,4351,4354],{"className":4350},[630,743],[569,4352,598],{"className":4353},[630,631,743],[569,4355,4357],{"className":4356},[1046],[569,4358,4360],{"className":4359},[718],[569,4361,4363],{"className":4362},[723],[569,4364,4367],{"className":4365,"style":4366},[727],"height:0.7463em;",[569,4368,4370,4374],{"style":4369},"top:-2.786em;margin-right:0.0714em;",[569,4371],{"className":4372,"style":4373},[735],"height:2.5em;",[569,4375,4379],{"className":4376},[740,4377,4378,743],"reset-size3","size1",[569,4380,2000],{"className":4381},[630,743],[569,4383,2005],{"className":4384},[2107,743],[569,4386,4388,4391],{"className":4387},[630,743],[569,4389,605],{"className":4390,"style":652},[630,631,743],[569,4392,4394],{"className":4393},[1046],[569,4395,4397],{"className":4396},[718],[569,4398,4400],{"className":4399},[723],[569,4401,4403],{"className":4402,"style":4366},[727],[569,4404,4405,4408],{"style":4369},[569,4406],{"className":4407,"style":4373},[735],[569,4409,4411],{"className":4410},[740,4377,4378,743],[569,4412,2000],{"className":4413},[630,743],[569,4415,4416,4419],{"style":756},[569,4417],{"className":4418,"style":736},[735],[569,4420],{"className":4421,"style":764},[763],[569,4423,4424,4427],{"style":767},[569,4425],{"className":4426,"style":736},[735],[569,4428,4430],{"className":4429},[740,741,742,743],[569,4431,4433,4436],{"className":4432},[630,743],[569,4434,598],{"className":4435},[630,631,743],[569,4437,605],{"className":4438,"style":652},[630,631,743],[569,4440,787],{"className":4441},[786],[569,4443,4445],{"className":4444},[723],[569,4446,4448],{"className":4447,"style":969},[727],[569,4449],{},[569,4451],{"className":4452},[656,711]," mit ",[569,4455,4457,4485],{"className":4456},[572],[569,4458,4460],{"className":4459},[576],[578,4461,4462],{"xmlns":580},[582,4463,4464,4482],{},[585,4465,4466,4468,4470,4472,4474,4476,4478,4480],{},[588,4467,590],{},[592,4469,595],{"stretchy":594},[1178,4471,1271],{},[592,4473,602],{"separator":601},[1178,4475,1271],{},[592,4477,608],{"stretchy":594},[592,4479,1445],{},[1178,4481,1271],{},[610,4483,4484],{"encoding":612},"f(0, 0) = 0",[569,4486,4488,4524],{"className":4487,"ariaHidden":601},[617],[569,4489,4491,4494,4497,4500,4503,4506,4509,4512,4515,4518,4521],{"className":4490},[621],[569,4492],{"className":4493,"style":626},[625],[569,4495,590],{"className":4496,"style":632},[630,631],[569,4498,595],{"className":4499},[636],[569,4501,1271],{"className":4502},[630],[569,4504,602],{"className":4505},[643],[569,4507],{"className":4508,"style":648},[647],[569,4510,1271],{"className":4511},[630],[569,4513,608],{"className":4514},[656],[569,4516],{"className":4517,"style":1470},[647],[569,4519,1445],{"className":4520},[1474],[569,4522],{"className":4523,"style":1470},[647],[569,4525,4527,4530],{"className":4526},[621],[569,4528],{"className":4529,"style":2760},[625],[569,4531,1271],{"className":4532},[630]," hat im Ursprung beide partiellen Ableitungen, ist dort aber nicht stetig.",{"title":4535,"searchDepth":4536,"depth":4536,"links":4537},"",2,[4538,4539,4540],{"id":562,"depth":4536,"text":563},{"id":1962,"depth":4536,"text":1963},{"id":3632,"depth":4536,"text":3633},[4542,4544,4546,4550,4553,4555,4557,4559],{"lhs":4543,"rhs":1271},"round(((x + 1e-5)^2*y + 3*(x + 1e-5)*y^3 - ((x - 1e-5)^2*y + 3*(x - 1e-5)*y^3)) \u002F (2e-5) - (2*x*y + 3*y^3), 6)",{"lhs":4545,"rhs":1271},"round((x^2*(y + 1e-5) + 3*x*(y + 1e-5)^3 - (x^2*(y - 1e-5) + 3*x*(y - 1e-5)^3)) \u002F (2e-5) - (x^2 + 9*x*y^2), 6)",{"lhs":4547,"rhs":2655,"where":4548},"2*x*y + 3*y^3",{"x":4549,"y":4536},1,{"lhs":4551,"rhs":2823,"where":4552},"x^2 + 9*x*y^2",{"x":4549,"y":4536},{"lhs":4554,"rhs":1271},"round((2*x*(y + 1e-5) + 3*(y + 1e-5)^3 - (2*x*(y - 1e-5) + 3*(y - 1e-5)^3)) \u002F (2e-5) - (2*x + 9*y^2), 6)",{"lhs":4556,"rhs":1271},"round(((x + 1e-5)^2 + 9*(x + 1e-5)*y^2 - ((x - 1e-5)^2 + 9*(x - 1e-5)*y^2)) \u002F (2e-5) - (2*x + 9*y^2), 6)",{"lhs":4558,"rhs":1271},"round((sin((x + 1e-5)*y) - sin((x - 1e-5)*y)) \u002F (2e-5) - y*cos(x*y), 6)",{"lhs":4560,"rhs":2000,"where":4561},"y*cos(x*y)",{"x":4562,"y":4536},0,"f\\colon D \\subseteq \\mathbb{R}^2 \\to \\mathbb{R},\\ (x_0, y_0) \\text{ innerer Punkt von } D,\\ \\text{der Grenzwert existiert}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmspace>\u003C\u002Fmspace>\u003Cmspace width=\"0.1111em\"\u002F>\u003Cmo lspace=\"0em\" rspace=\"0.17em\">\u003C\u002Fmo>\u003Cmtext> ⁣\u003C\u002Fmtext>\u003Cmo lspace=\"0em\" rspace=\"0em\">:\u003C\u002Fmo>\u003Cmspace width=\"0.3333em\"\u002F>\u003Cmi>D\u003C\u002Fmi>\u003Cmo>⊆\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\\colon D \\subseteq \\mathbb{R}^2 \\to \\mathbb{R},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1111em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:-0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">:\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\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:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(x_0, y_0)\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=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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\">0\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;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\">0\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">innerer Punkt von\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>D\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">D,\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">der Grenzwert existiert\u003C\u002Fspan>",null,"md","partial-derivative","\\frac{\\partial f}{\\partial x}(x_0, y_0) = \\lim_{h \\to 0} \\frac{f(x_0 + h,\\, y_0) - f(x_0, y_0)}{h}","\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>\u003Cmfrac>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo 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stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\frac{\\partial f}{\\partial x}(x_0, y_0) = \\lim_{h \\to 0} \\frac{f(x_0 + h,\\, y_0) - f(x_0, y_0)}{h}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0574em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord 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\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;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\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;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\">0\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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 mathnormal\" 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