Exercise ID258

Mathematical analysis → Derivation → Derivatives of composite functions
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Compute the derivative of the given function below.

y=ln cos x·sin22x

y=ln cos x sin22x g=cos x·sin22x    y=ln g y'=1g·g' g=cos x·sin2x=u·v    u=cos x  ;  v=sin22x   g'=u'·v+u·v' u=cos x  ;  v=sin22x   u'=-sin x ;  v'=2·sin 2x·cos 2x·2=4·sin 2x·cos 2x g'=-sin x·sin22x+cos x·4·sin 2x·cos2x y'=1cos x sin22x·-sin x·sin22x+cos x·4·sin 2x·cos2x y'=1cos x sin22x·sin 2x·4·cos x·cos2x-sin x·sin2x y'=4 ·cos 2x·cosx-sin x·sin 2xcos x·sin 2x y'=4 ·cos 2x·cosxcos x·sin 2x- sin x·sin 2xcos x·sin 2x y'=4 ·cos 2xsin 2x- sin xcos x y'=4 ctg 2x-tg x
y'=4 ctg 2x-tg x

ddxfgx=dfdg·dgdx=f'g·g'x

ddxln x=1x

ddxxn=nxn-1

ddxsin x=cos x

ddxcos x=-sin x

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