三角函数、导数、微分、积分

三角函数诱导公式tgA=tanA=aacossinaasin)sin(sin(2-a)=cosasin(2+a)=cosasin(π-a)=sinasin(π+a)=-sinacos(-a)=cosacos(2-a)=sinacos(2+a)=-sinacos(π-a)=-cosacos(π+a)=-cosa两角和差公式sin(A+B)=sinAcosB+cosAsinBcos(A+B)=cosAcosB-sinAsinBsin(A-B)=sinAcosB-cosAsinBcos(A-B)=cosAcosB+sinAsinBtan(A+B)=tanAtanB-1tanBtanAcot(A+B)=cotAcotB1-cotAcotBtan(A-B)=tanAtanB1tanBtanAcot(A-B)=cotAcotB1cotAcotB倍角公式三倍角公式半角公式tan2A=Atan12tanA2sin3A=3sinA-4(sinA)3sin(2A)=2cos1ASin2A=2SinA•CosAcos3A=4(cosA)3-3cosAcos(2A)=2cos1ACos2A=Cos2A-Sin2A=2Cos2A-1=1-2sin2Atan3a=tana·tan(3+a)·tan(3-a)tan(2A)=AAcos1cos1cot(2A)=AAcos1cos1tan(2A)=AAsincos1=AAcos1sin和差化积积化和差sina+sinb=2sin2bacos2basinasinb=-21[cos(a+b)-cos(a-b)]sina-sinb=2cos2basin2bacosacosb=21[cos(a+b)+cos(a-b)]cosa+cosb=2cos2bacos2basinacosb=21[sin(a+b)+sin(a-b)]cosa-cosb=-2sin2basin2bacosasinb=21[sin(a+b)-sin(a-b)]tana+tanb=babacoscos)sin(万能公式sina=2)2(tan12tan2aacosa=22)2(tan1)2(tan1aatana=2)2(tan12tan2aa其他非重点三角函数csc(a)=asin1aa22csc1cotsec(a)=acos1aaa222cos1sec1tan双曲函数sinh(a)=2e-e-aacosh(a)=2ee-aatgh(a)=)cosh()sinh(aa等价无穷小xx~sinxxxarctan~~arcsinxx~)1ln(xex~1xx~tan2~cos12xxuxxu~1)1(nxxn~11axaxln~1两个重要的极限1sinlim0xxxexxx)11(lim导数、微分、积分函数的和差积商求导法则函数的和差积商微分法则函数的和差积商求导法则'''vuvudvduvud)()1(11ucuxdxxuu''CuCuCduCud)(dxxfkdxxkf'''uvvuuvudvvduuvd)(dxxgdxxfdxxgxf2'''vuvvuvu2)(vudvvduvudxuduufdxxxf'高阶导数函数)(xfy的导数)(''xfy称为一阶导数，记作'y或dxdy；把)(''xfy的导数称为二阶导数，记作''yy或22dxyd＝dxdydxd；类似的，二阶导数的导数称为三阶导数；三阶导数的导数称为四阶导数；（n－1）导数的导数叫做n阶导数记作nndxyd导数公式微分公式积分公式0'Cdxxfdy)('Ckxkdx1')(uuuxxdxuxxduu1)(Cuxdxxuu112'1)1(xxdxd()Cxdxxln1xxcos)(sin'xdxxdcos)(sinCxxdxsincosxxsin)(cos'xdxxdsin)(cosCxxdxcossinxx2'sec)(tanxdxxd2sec)(tanCxxdxdxxtanseccos122Cxxdxcoslntanxx2'csc)(cotxdxxd2csc)(cotCxxdxdxxcotcscsin122Cxxdxsinlncotxxxtansec)(sec'xdxxxdtansec)(secCxxxdxtanseclnsecCxxdxxsectansecxxxcotcsc)(csc'xdxxxdcotcsc)(cscCxxxdxcotcsclncscCxxdxxcsccotcscaaaxxln)('adxaadxxln)(Caadxaxxlnxxee')(dxeedxx)(Cedxexxaxxaln1)(log'dxaxxdaln1)(logCdxxx1)(ln'dxxxd1)(lnCxdxxln12'11)(arcsinxxdxxxd211)(arcsinCxdxxarcsin1122'11)(arccosxxdxxxd211)(arccosCdx2'11)(arctanxxdxxxd211)(arctanCxdxxarctan1122'11)cot(xxarcdxxarcd211cot)(Cdxchxshx')(dxd()Cchxshxdxshxchx')(Cshxchxdxxchthx2'1)(Caxadxxaarctan11222'11)(xarshxCaxaxadxaxln2112211)(2'xarchxCaxdxxaarcsin1222'11)(xarthxCaxxdxax)ln(12222Caxxdxax2222ln1