Given that y=sin(x^x)

Let x^x=u, then y=sin u

Differentiating with respect to x, we get

–(1)

Also, u=x^x

Taking log both sides, we get

Log_e u=x × log_e x

Differentiating with respect to x, we get

⇒ -(2)

From (1) and (2), we get