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Question

Find the derivative of the following function:
f(x) = sin x+cos xsin xcos x

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Solution

Here f(x)=sin x+cos xsin xcos x

f(x)=ddx[sin x+cos xsin xcos x]

=(sin xcos x)ddx(sin x+cos x)(sin x+cos x)ddx(sin xcos x)(sin xcos x)2

=(sin xcos x)(cos xsin x)(sin x+cos x)(cos x+sin x)(sin xcos x)2

=(sin xcos x)2(sin x+cos x)2(sin xcos x)2

=2(sin2x+cos2x)(sin xcos x)2

=2(sin xcos x)2

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