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Question

Differentiate given problems w.r.t.x.
(sin xcos x)(sin xcos x)


Solution

Let  y=(sin xcos x)(sin xcos x)

Taking log on both sides w.r.t.x, we get 

log y = log(sin xcos x)(sin xcos x)

or   logy=(sinxcosx)log(sinxcosx)(logmn=n log.m)

Differentiating both sides w.r.t.x, we obtain

1ydydx=(sinxcosx)cos x+sin xsin xcos x+[log(sinxcosx)](cosx+sinx)

dydx=y(cosx+sinx)[1+log(sin xcos x)]

=(cosx+sinx)(sinxcosx)(sinxcosx)1+log(sinxcosx)

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