微积分基本公式

微积分基本公式微积分基本公式微积分基本公式微积分基本公式编制仅供参考审核批准生效日期地址：电话：传真:邮编:微积分公式Dxsinx=cosxcosx=-sinxtanx=sec2xcotx=-csc2xsecx=secxtanxcscx=-cscxcotxsinxdx=-cosx+Ccosxdx=sinx+Ctanxdx=ln|secx|+Ccotxdx=ln|sinx|+Csecxdx=ln|secx+tanx|+Ccscxdx=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()=cos-1()=tan-1()=cot-1()=sec-1()=csc-1()=sin-1xdx=xsin-1x++Ccos-1xdx=xcos-1x-+Ctan-1xdx=xtan-1x-

ln(1+x2)+Ccot-1xdx=xcot-1x+?ln(1+x2)+Csec-1xdx=xsec-1x-ln|x+|+Ccsc-1xdx=xcsc-1x+ln|x+|+Csinh-1()=ln(x+)xRcosh-1()=ln(x+)x≧1tanh-1()=ln()|x|<1coth-1()=ln()|x|>1sech-1()=ln(+)0≦x≦1csch-1()=ln(+)|x|>0Dxsinhx=coshxcoshx=sinhxtanhx=sech2xcothx=-csch2xsechx=-sechxtanhxcschx=-cschxcothxsinhxdx=coshx+Ccoshxdx=sinhx+Ctanhxdx=ln|coshx|+Ccothxdx=ln|sinhx|+Csechxdx=-2tan-1(e-x)+Ccschxdx=2ln||+Cduv=udv+vduduv=uv=udv+vdu→udv=uv-vducos2θ-sin2θ=cos2θcos2θ+sin2θ=1cosh2θ-sinh2θ=1cosh2θ+sinh2θ=cosh2θDxsinh-1()=cosh-1()=tanh-1()=coth-1()=sech-1()=csch-1()=sinh-1xdx=xsinh-1x-+Ccosh-1xdx=xcosh-1x-+Ctanh-1xdx=xtanh-1x+

ln|1-x2|+Ccoth-1xdx=xcoth-1x-

ln|1-x2|+Csech-1xdx=xsech-1x-sin-1x+Ccsch-1xdx=xcsch-1x+sinh-1x+CaγaγRαβcbRαβcbsin3θ=3sinθ-4sin3θcos3θ=4cos3θ-3cosθ→sin3θ=(3sinθ-sin3θ)→cos3θ=(3cosθ+cos3θ)sinx=cosx=sinhx=coshx=正弦定理:===2R余弦定理:a2=b2+c2-2bccosαb2=a2+c2-2accosβc2=a2+b2-2abcosγsin(α±β)=sinαcosβ±cosαsinβcos(α±β)=cosαcosβsinαsinβ2sinαcosβ=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=2sin(

α+β)cos(

α-β)sinα-sinβ=2cos(

α+β)sin(

α-β)cosα+cosβ=2cos(

α+β)cos(

α-β)cosα-cosβ=-2sin(

α+β)sin(

α-β)tan(α±β)=,cot(α±β)=ex=1+x+++…++…sinx=x-+-+…++…cosx=1-+-+…++…ln(1+x)=x-+-+…++…tan-1x=x-+-+…++…(1+x)r=1+rx+x2+x3+…-1<x<1=n=n(n+1)=n(n+1)(2n+1)=[n(n+1)]2Γ(x)=x-1e-tdt=22x-1dt=x-1dtβ(m,n)=m-1(1-x)n-1dx=22m-1xcos2n-1xdx=dx希腊字母(GreekAlphabets)大写小写读音大写小写读音大写小写读音ΑαalphaΙιiotaΡρrhoΒβbetaΚκkappaΣσ,sigmaΓγgammaΛλlambdaΤτtauΔδdeltaΜμmuΥυupsilonΕεepsilonΝνnuΦφphiΖζzetaΞξxiΧχkhiΗηetaΟοomicronΨψpsiΘθthetaΠπpiΩωomega倒数关系:sinθcscθ=1;tanθcotθ=1;cosθsecθ=1商数关系:tanθ=;cotθ=平方关系:cos2θ+sin2θ=1;tan2θ+1=sec2θ;1+cot2θ=csc2θ;顺位高d顺位低;0*=*==0*==;=;=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)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)调和平均数(Harmonicmean)平均差(AverageDeviatoin)变异数(Variance)or标准差(StandardDeviation)or

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)DiscreteUniform(n+1)(n2+1)ContinuousUniform(a+b)(b-a)2Bernoullipxq1-x(x=0,1)ppqq+petBinomialpxqn-xnpnpq(q+pet)nNegativeBinomialpkqxMultinomialf(x1,x2,…,xm-1)=npinpi(1-pi)三项

(p1et1+p2et2+p3)nGeometricpqx-1HypergeometricnnPoissonλλNormalμσ2BetaGammaExponentChi-Squaredχ2=f(χ2)

=E(χ2)=nV(χ2)=2nWeibull10000000000000000000000001024yottaY

10000000000000000000001021zettaZ

10000000000000000001018exaE

10000000000000001015petaP

10000000000001012teraT兆

1000000000109gigaG十亿

1000000106megaM百万

1000103kiloK千

100102hectoH百

10101decaD十

10-1decid分，十分之一

10-2centic厘（或写作「厘」），百分之一

10-3millim毫，千分之一

00110-6micro微，百万分之一

00000110-9nanon奈，十亿分之一