数-学-微-积-分-公-式-表

数学微积分公式表导数公式()()Fxfx积分公式()()fxdxFxC凑微分公式()()fxdxdFx1．0C0dxC0dxdC2．1)(xx（为实数）111xdxxC(1)111xdxdx特别：()1x1dxxC1()dxdxc1()2xx12dxxCx12dxdxx211()xx211dxCxx211()dxdxx3．)1,0(ln)(aaaaaxx1lnxxadxaCa1()lnxxadxdaa特别：xxee)(；xxedxeCxxedxde41(log)(0,1)lnaxaaxa特别：xx1)(ln；1lndxxCx1lndxdxx5．xxcos)(sin；cossinxdxxCcossinxdxdx6．xxsin)(cos；sincosxdxxCsin(cos)xdxdx7．xxx22seccos1)(tan2sectanxdxxC2sectanxdxdx8．xxx22cscsin1)(cot2csccotxdxxC2csc(cot)xdxdx9.xxxtansec)(secsectansecxxdxxCsectansecxxdxdx10.xxxcotcsc)(csccsccotcscxxdxxCcsccot(csc)xxdxdx11.211)(arcsinxx2arcsin1dxxCx2arcsin1dxxCx12.211)(arccosxx2arccos1dxxCx2(arccos)1dxdxx13.211)(arctanxx2arctan1dxxCx2arctan1dxdxx14.211)cot(xxarc2arccot1dxxCx2(arccot)1dxdxx15.()axCaadxaxC()adxdaxC补充1：221arctandxxCaxaa补充2：221ln2dxaxCaxaax补充3：221ln2dxxaCxaaxa补充4：22arcsindxxCaax补充5：tanlncosxdxxC补充6：cotlnsinxdxxC补充7：seclnsectanxdxxxC补充8：csclncsccotxdxxxC求导法则：[()()]uxvx()()uxvx[()()]()()()()uxvxuxvxuxvx[()()()]()()()()()()()()()uxvxwxuxvxwxuxvxwxuxvxwx推论)())((xuCxCu（C为常数）．2()()()()()(()0)()()uxuxvxuxvxvxvxvx初等数学中部分常用公式1.乘法和因式分解22332232233222332bababababababababbaababababa2.指数其中a、b为正实数，m、n为任意数nmnmmmaaaaaa.31.21.10mnnmnmmnnmnmnmaaaaaaaa.6.5.43．对数1,aoalog1.log10.;2log13.;log4.log;0,1;logaaaxbabaaxxxbba5.logloglog6.logloglog7.loglogaaaaaaaaaxyxyxxyyxax4．三角函数基本公式aaaaaaaaaaaacotsincos.5tancossin.4csccot1.3sectan1.21cossin.1222222aaaaaacos1sec.8sin1csc.7tan1cot.65．倍角公式1cos2sin21sincos2cos.2cossin22sin.12222aaaaaaaa6．度与弧度18011180度弧度；弧度度；0000304560906462；；；；7．特殊角的三角函数值sincostancotseccsc0010不存在1不存在621233333322422221122323213332332210不存在0不存在10—10不存在—1不存在23—10不存在0不存在—1010不存在1不存在