Q. 184.7( 3 Votes )

Differentiate the

Answer :

Let,

y = x^{sin x} + (sin x)^{cos x}

Let, u = x^{sin x}

v = (sin x)^{cos x}

y = u + v

Now,

u = x^{sin x}

Taking log both sides,

log u = log (x^{sin 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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