高数微积分公式大全

微積分公式Dxsinx=cosxcosx=-sinxtanx=sec2xcotx=-csc2xsecx=secxtanxcscx=-cscxcotxsinxdx=-cosx+Ccosxdx=sinx+Ctanxdx=ln|secx|+Ccotxdx=ln|sinx|+Csecxdx=ln|secx+tanx|+Ccscxdx=ln|cscx–cotx|+Csin-1(-x)=-sin-1xcos-1(-x)=-cos-1xtan-1(-x)=-tan-1xcot-1(-x)=-cot-1xsec-1(-x)=-sec-1xcsc-1(-x)=-csc-1xDxsin-1(ax)=221xacos-1(ax)=tan-1(ax)=22xaacot-1(ax)=sec-1(ax)=22axxacsc-1(x/a)=sin-1xdx=xsin-1x+21x+Ccos-1xdx=xcos-1x-21x+Ctan-1xdx=xtan-1x-½ln(1+x2)+Ccot-1xdx=xcot-1x+½ln(1+x2)+Csec-1xdx=xsec-1x-ln|x+12x|+Ccsc-1xdx=xcsc-1x+ln|x+12x|+Csinh-1(ax)=ln(x+22xa)xRcosh-1(ax)=ln(x+22ax)x≧1tanh-1(ax)=a21ln(xaxa)|x|1coth-1(ax)=a21ln(axax)|x|1sech-1(ax)=ln(x1+221xx)0≦x≦1csch-1(ax)=ln(x1+221xx)|x|0Dxsinhx=coshxcoshx=sinhxtanhx=sech2xcothx=-csch2xsechx=-sechxtanhxcschx=-cschxcothxsinhxdx=coshx+Ccoshxdx=sinhx+Ctanhxdx=ln|coshx|+Ccothxdx=ln|sinhx|+Csechxdx=-2tan-1(e-x)+Ccschxdx=2ln|xxee211|+Cduv=udv+vduduv=uv=udv+vdu→udv=uv-vducos2θ-sin2θ=cos2θcos2θ+sin2θ=1cosh2θ-sinh2θ=1cosh2θ+sinh2θ=cosh2θDxsinh-1(ax)=221xacosh-1(ax)=221axtanh-1(ax)=22xaacoth-1(ax)=sech-1(ax)=22xaxacsch-1(x/a)=22xaxasinh-1xdx=xsinh-1x-21x+Ccosh-1xdx=xcosh-1x-12x+Ctanh-1xdx=xtanh-1x+½ln|1-x2|+Ccoth-1xdx=xcoth-1x-½ln|1-x2|+Csech-1xdx=xsech-1x-sin-1x+Ccsch-1xdx=xcsch-1x+sinh-1x+Csin3θ=3sinθ-4sin3θcos3θ=4cos3θ-3cosθ→sin3θ=¼(3sinθ-sin3θ)→cos3θ=¼(3cosθ+cos3θ)sinx=jeejxjx2cosx=2jxjxeesinhx=2xxeecoshx=2xxee正弦定理:sina=sinb=sinc=2R餘弦定理:a2=b2+c2-2bccosαb2=a2+c2-2accosβc2=a2+b2-2abcosγabcαβγRsin(α±β)=sinαcosβ±cosαsinβcos(α±β)=cosαcosβsinαsinβ2sinαcosβ=sin(α+β)+sin(α-β)2cosαsinβ=sin(α+β)-sin(α-β)2cosαcosβ=cos(α-β)+cos(α+β)2sinαsinβ=cos(α-β)-cos(α+β)sinα+sinβ=2sin½(α+β)cos½(α-β)sinα-sinβ=2cos½(α+β)sin½(α-β)cosα+cosβ=2cos½(α+β)cos½(α-β)cosα-cosβ=-2sin½(α+β)sin½(α-β)tan(α±β)=tantantantan,cot(α±β)=cotcotcotcotex=1+x+!22x+!33x+…+!nxn+…sinx=x-!33x+!55x-!77x+…+)!12()1(12nxnn+…cosx=1-!22x+!44x-!66x+…+)!2()1(2nxnn+…ln(1+x)=x-22x+33x-44x+…+)!1()1(1nxnn+…tan-1x=x-33x+55x-77x+…+)12()1(12nxnn+…(1+x)r=1+rx+!2)1(rrx2+!3)2)(1(rrrx3+…-1x1ni11=nnii1=½n(n+1)nii12=61n(n+1)(2n+1)nii13=[½n(n+1)]2Γ(x)=0tx-1e-tdt=20t2x-12tedt=0)1(lntx-1dtβ(m,n)=10xm-1(1-x)n-1dx=220sin2m-1xcos2n-1xdx=01)1(nmmxxdx希腊字母(GreekAlphabets)大写小写读音大写小写读音大写小写读音ΑαalphaΙιiotaΡρrhoΒβbetaΚκkappaΣσ,ςsigmaΓγgammaΛλlambdaΤτtauΔδdeltaΜμmuΥυupsilonΕεepsilonΝνnuΦφphiΖζzetaΞξxiΧχkhiΗηetaΟοomicronΨψpsiΘθthetaΠπpiΩωomega倒数关系:sinθcscθ=1;tanθcotθ=1;cosθsecθ=1商数关系:tanθ=cossin;cotθ=sincos平方关系:cos2θ+sin2θ=1;tan2θ+1=sec2θ;1+cot2θ=csc2θ順位低順位高;顺位高d顺位低;0*=1*==0*01=0000=)(0e;0=0e;1=0e顺位一:对数;反三角(反双曲)顺位二:多项函数;幂函数顺位三:指数;三角(双曲)算术平均数(Arithmeticmean)nXXXXn...21中位数(Median)取排序后中间的那位数字众数(Mode)次数出现最多的数值几何平均数(Geometricmean)nnXXXG...21调和平均数(Harmonicmean))1...11(1121nxxxnH平均差(AverageDeviatoin)nXXni||1变异数(Variance)nXXni21)(or1)(21nXXni标准差(StandardDeviation)nXXni21)(or1)(21nXXni分配机率函数f(x)期望值E(x)变异数V(x)动差母函数m(t)DiscreteUniformn121(n+1)121(n2+1)tntteeen1)1(1ContinuousUniformab121(a+b)121(b-a)2tabeeatbt)(Bernoullipxq1-x(x=0,1)ppqq+petBinomialxnpxqn-xnpnpq(q+pet)nNegativeBinomialxxk1pkqxpkq2pkqktkqep)1(Multinomialf(x1,x2,…,xm-1)=mxmxxmpppxxxn...!!...!!212121npinpi(1-pi)三項(p1et1+p2et2+p3)nGeometricpqx-1p12pqttqepe1HypergeometricnNxnkNxknNk1NnNnNkPoisson!xexλλ)1(teeNormal2)(2121xeμσ22221tteBeta11)1(),(1xxB2))(1(Gammaxex1)()(2tExponentxe121tChi-Squaredχ2=f(χ2)=212222)(221ennnE(χ2)=nV(χ2)=2n2)21(ntWeibullxe111111122210000000000000000000000001024yottaY10000000000000000000001021zettaZ10000000000000000001018exaE10000000000000001015petaP10000000000001012teraT兆1000000000109gigaG十亿1000000106megaM百万1000103kiloK千100102hectoH百10101decaD十0.110-1decid分，十分之一0.0110-2centic厘（或写作「厘」），百分之一0.00110-3millim毫，千分之一0.00000110-6micro?微，百万分之一0.00000000110-9nanon奈，十亿分之一0.00000000000110-12picop皮，兆分之一0.00000000000000110-15femtof飞（或作「费」），千兆分之一0.00000000000000000110-18attoa阿0.00000000000000000000110-21zeptoz0.00000000000000000000000110-24yoctoy