Transcription of Common Derivatives Integrals - Lamar University
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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/Logarithm Functions ()()lnxxdaaadx= ()xxddx=ee ()()1ln,0dxxdxx=> ()1ln,0dxxdxx= ()()1log,0lnadxxdxxa=> Hyperbolic Trig Functions ()sinhcoshdxxdx= ()coshsinhdxxdx= ()2tanhsechdxxdx= ()sechsechtanhdxxxdx=- ()cschcschcothdxxxdx=- ()
Note that all but the first one of these tend to be taught in a Calculus II class. u Substitution Given (())() b a ò fgxg¢ xdx then the substitution u=gx( ) will convert this into the integral, (())() () bgb( ) aga òòfgxg¢ xdx= fudu . Integration by Parts The standard formulas for integration by parts are, bbb aaa òudv=uv-vduòòudv=-uvvdu
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