Common Derivatives Integrals - Lamar University

Common Derivatives and Integrals Visit for a complete set of Calculus I & II notes. 2005 Paul Dawkins Derivatives Basic properties /Formulas/Rules ()()()dcfxcfxdx =, c is any constant. ()()()()()fxgxfxgx = ()1nndxnxdx-=, n is any number. ()0dcdx=, c is any constant. ()fgfgfg =+ (Product Rule) 2ffgfggg -= (Quotient Rule) ()()()()()()dfgxfgxgxdx = (Chain Rule) ()()()()gxgxdgxdx =ee ()()()()lngxdgxdxgx = Common Derivatives Polynomials ()0dcdx= ()1dxdx= ()dcxcdx= ()1nndxnxdx-= ()1nndcxncxdx-= Trig Functions ()sincosdxxdx= ()cossindxxdx=- ()2tansecdxxdx= ()secsectandxxxdx= ()csccsccotdxxxdx=- ()2cotcscdxxdx=- Inverse Trig Functions ()121sin1dxdxx-=- ()121cos1dxdxx-=-- ()121tan1dxdxx-=+ ()121sec1dxdxxx-=- ()121csc1dxdxxx-=-- ()121cot1dxdxx-=-+ Exponential/Loga

Basic Properties/Formulas/Rules òòcf(x)dx= cf(x)dx, c is a constant. òf(x)–g(x)dx=–òòf(x)dxg(x)dx b() ()b () a òfxdx=Fx=-FbFa where F(x) = ò f(x)dx bb() aa òòcfxdx= cfxdx, c is a constant. () () bbb aaa òfx–gxdx=–òòfxdxgxdx 0 a a ò fxdx = () ba ab òòfxdx=- fxdx b() cb() aac òfxdx=+òòfxdxfxdx b a òcdx=-cba

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