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Question

Find the derivative of sinxxcosxxsinx+cosx

A
x2(xsinx+cosx)2
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B
x2(xsinx+cosx)2
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C
x2(cosxsinx)(xsinx+cosx)2
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D
x2(cosx+sinx)(xsinx+cosx)2
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Solution

The correct option is A x2(xsinx+cosx)2
ddx(sinxxcosxxsinx+cosx)
=(xsinx+cosx)ddx(sinxxcosx)(sinxxcosx)ddx(xsinx+cosx)(xsinx+cosx)2
=(xsinx+cosx)[cosx(xsinx+cosx)](sinxxcosx)[(xcosx+sinx)sinx](xsinx+cosx)2
=xsinx(xsinx+cosx)xcosx(sinxxcosx)(xsinx+cosx)2
=x2(sin2x+cos2x)+xsinxcosxxsinxcosx(xsinx+cosx)2
=x2(xsinx+cosx)2

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