微分学中的符号“dx”、“dy”等,系由莱布尼茨首先使用.其中的d源自拉丁语中“差”（Differentia）的第一个字母.积分符号“∫”亦由莱布尼茨所创,它是拉丁语“总和”（Summe）的第一个字母s的伸长(和∑有相同的意义).lim就是limit的缩写,是极限的意思,lim下面符号的意思是“当x趋近于零时”f'（x）则表示f(x)的导数,也就是变化率,从几何意义上讲,就是f(x)的函数图像在x处切线的斜率.

　　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(x/a)=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|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(x/a)=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+Csin3θ=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=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