Transcription of nn) (cx ncx nn) - Lamar University
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nn) (cx ncx nn) - Lamar University
Common Derivatives and Integrals Visit for a complete set of Calculus I & II notes. 2005 Paul Dawkins Derivatives Basic Properties/Formulas/Rules ()()( )dcf xcfxdx =, c is any constant. ()( )()() ()fxgx fxgx = ( )1nndxnxdx =, n is any number. ()0dcdx=, c is any constant. ( )fgf g fg = + (Product Rule) 2ff g fggg = (Quotient Rule) ( )()()( )()()df gxf gx g xdx = ( Chain Rule) ( )()( )()gxgxdgxdx =ee ( )()( )( )lngxdgxdxg x = Common Derivatives Polynomials ( )0dcdx= ( )1dxdx= ()dcxcdx= ( )1nndxnxdx = ( )1nndcxncxdx = Trig Functions ()sincosdxxdx= ()cossindxxdx= ()2tansecdxxdx= ()secsec tandxxxdx= ()csccsc cotdxxxdx= ()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= ()sechsech tanhdxxxdx= ()cschcsch cothdxxxdx= ()
Integration by Parts The standard formulas for integration by parts are, bb b aa a ∫∫ ∫ ∫udv uv vdu=−= udv uv vdu− Choose uand then compute and dv du by differentiating u and compute v by using the fact that v dv=∫.
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