基本初等函数求导公式 (1) 0)(C (2) 1)(xx (3) xxcos)(sin (4) xxsin)(cos (5) xx2sec)(tan (6) xx2csc)(cot (7) xxxtansec)(sec (8) xxxcotcsc)(csc (9) aaaxxln)( (10) (e )exx (11) axxaln1)(log (12) xx1)(ln, (13) 211)(arcsinxx (14) 211)(arccosxx (15) 21(arctan )1xx (16) 21(arccot )1xx 函数的和、差、积、商的求导法则 设)(xuu , )(xvv 都可导,则 (1) vuvu )( (2) uCCu)((C 是常数) (3) vuvuuv)( (4) 2vvuvuvu 反函数求导法则 若函数)(yx在某区间yI内可导、单调且0)( y,则它的反函数)(xfy 在对应区间xI 内也可导,且 )(1)(yxf 或 dydxdxdy1 复合函数求导法则 设)(ufy ,而)(xu且)(uf及)(x都可导,则复合函数)]([xfy的导数为 dydy dudxdu dx或 2. 双曲函数与反双曲函数的导数. 双曲函数与反双曲函数都是初等函数,它们的导数都可以用前面的求导公式和求导法则求出. 可以推出下表列出的公式: (sh )chxx (ch )shxx 21(th )chxx 21(arsh )1xx 21(arch )1xx 21(arth )1xx 常用积分公式表·例题和点评 ⑴dk xkxc (k 为常数) ⑵11d (1)1xxxc 特别,211dxcxx , 322d3xxxc, 1 d2xxcx ⑶1 dln ||xxcx ⑷dlnxxaaxca, 特别,e dexxxc ⑸sindcosx xxc ⑹cosdsinx xxc ⑺221dcscdcotsinxx xxcx ⑻221dsecdtancosxx xxcx ⑼221darcsin(0)xxc aaax,特别,21darcsin1xxcx ⑽2211darctan(0)xxc aaaax,特别,21darctan1xxcx ⑾2211dln(0)2axxc aaaxax 或2211dln(0)2xaxc aaxaxa ⑿tandln cosx xxc ⒀cotdln sinx xxc ⒁ln csccot1csc ddln tansin2xxcx xxxcx ⒂ln sectan1sec ddln tancos24xxcx xxxcx ⒃(0)221daxxa22ln xxac ⒄2(0)2222darcsin22aaxxa...