Question

Differentiate with respect to $x$:
$\sin \left(x^x\right)$

Answer 1

$y=\sin x^x$

Consider $z=x^x$

Taking log on both sides

$\log z=x\log x$

$\frac{1}{z}\frac{dz}{dx}=1+\log x$

$\frac{dz}{dx}=x^x(1+\log x)$

Thus, $\frac{dy}{dx}=\cos \left(x^x\right).x^x(1+\log x)$