Solve this following

If $y=(\sin x)^{\cos x}+(\cos x)^{\sin x}$, prove tha $\frac{d y}{d x}=(\sin x)^{\cos x} \cdot[\cot x \cos x-\sin x$

$(\log \sin x)]+(\cos x)^{\sin x \cdot}[\cos x(\log \cos x)-\sin x \tan x]$