Q18 of 45 Page 1

Differentiate the following function w.r.t. x:

xsin x + (sin x)cos x .

Let,


y = xsin x + (sin x)cos x


Let, u = xsin x


v = (sin x)cos x


y = u + v



Now,


u = xsin x


Taking log both sides,


log u = log (xsin x)


⇒ log u = (sin x)(log x)


Differentiating both sides, we get





v = (sin x)cos x


Taking log both sides,


log v = log((sin x)cos x)


⇒ log v = (cos x) (log (sin x))





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