Differentiate the functions given in w.r.t. x.

x^x – 2^{sin x}

Given: x^x – 2^{sin x}

Let y= x^x – 2^{sin x}

Let y = u - v

⇒ u = x^x and v = 2^{sin x}

For, u = x^x

Taking log on both sides, we get

log u = log x^x

⇒log u = x.log(x)

Now, differentiate both sides with respect to x

For, v = 2^{sin x}

Taking log on both sides, we get

log v = log 2^{sin x}

⇒log v = sin x. log (2)

Now, differentiate both sides with respect to x

Because, y = u - v