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Question

Find the derivative of y=sinxxcosxcosx+xsinx

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Solution

y=sinxxcosxcosx+xsinx

dydx=(cosx+xsinx)ddx(sinxxcosx)(sinxxcosx)ddx(cosx+xsinx)(cosx+xsinx)2

=(cosx+xsinx)[cosx(xsin+cosx)](sinxxcosx)[sinx+xcosx+sinx](cosx+xsinx)2

=(cosx+2sinx)[cosx+xsinxcosx](sinxxcosx)[xcosx](cosx+xsinx)2

=xsinxcosx+x2sin2xxcosxsinx+x2cos2x(cosx+xsinx)2

=x2(sin2x+cos2x)(cosx+xsinx)2

=x2(cosx+xsinx)2[sin2+cos2x=1].

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