数学微积分公式表导数公式()()Fxfx积分公式()()fxdxFxC凑微分公式()()fxdxdFx1.0C0dxC0dxdC2.1)(xx(为实数)111xdxxC(1)111xdxdx特别:()1x1dxxC1()dxdxc1()2xx12dxxCx12dxdxx211()xx211dxCxx211()dxdxx3.)1,0(ln)(aaaaaxx1lnxxadxaCa1()lnxxadxdaa特别:xxee)(;xxedxeCxxedxde41(log)(0,1)lnaxaaxa特别:xx1)(ln;1lndxxCx1lndxdxx5.xxcos)(sin;cossinxdxxCcossinxdxdx6.xxsin)(cos;sincosxdxxCsin(cos)xdxdx7.xxx22seccos1)(tan2sectanxdxxC2sectanxdxdx8.xxx22cscsin1)(cot2csccotxdxxC2csc(cot)xdxdx9.xxxtansec)(secsectansecxxdxxCsectansecxxdxdx10.xxxcotcsc)(csccsccotcscxxdxxCcsccot(csc)xxdxdx11.211)(arcsinxx2arcsin1dxxCx2arcsin1dxxCx12.211)(arccosxx2arccos1dxxCx2(arccos)1dxdxx13.211)(arctanxx2arctan1dxxCx2arctan1dxdxx14.211)cot(xxarc2arccot1dxxCx2(arccot)1dxdxx15.()axCaadxaxC()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22332232233222332bababababababababbaababababa2.指数其中a、b为正实数,m、n为任意数nmnmmmaaaaaa.31.21.10mnnmnmmnnmnmnmaaaaaaaa.6.5.43.对数1,aoalog1.log10.;2log13.;log4.log;0,1;logaaaxbabaaxxxbba5.logloglog6.logloglog7.loglogaaaaaaaaaxyxyxxyyxax4.三角函数基本公式aaaaaaaaaaaacotsincos.5tancossin.4csccot1.3sectan1.21cossin.1222222aaaaaacos1sec.8sin1csc.7tan1cot.65.倍角公式1cos2sin21sincos2cos.2cossin22sin.12222aaaaaaaa6.度与弧度18011180度弧度;弧度度;0000304560906462;;;;7.特殊角的三角函数值sincostancotseccsc0010不存在1不存在621233333322422221122323213332332210不存在0不存在10—10不存在—1不存在23—10不存在0不存在—1010不存在1不存在