Differentiate each of the following w.r.t. x

(sin x)^{cos x}

Given: (Sin x)^{cos x}

To Find: Differentiate w.r.t x

We have (Sin x)^{cos x}

Let y=(Sin x)^{cos x}

Now, Taking Log on both sides, we get

Log y = cos x.log(sin x)

Now, Differentiate both side w.r.t. x

By using product rule of differentiation

Substitute the value of y , we get

y’ = (Sin x)^{cos x}[cos x.cot x - sin x (log sinx)]

Hence, y’ = (Sin x)^{cos x}[cos x.cot x - sin x (log sinx)]