SOLUTION —
Let $y=x^{\sin x}$
$\Rightarrow \quad \log y =\sin x \log x \\$
$\Rightarrow \frac{1}{y} \frac{d y}{d x} =\frac{\sin x}{x}+\log x \cos x \\$
$\Rightarrow \frac{d y}{d x} =x^{\sin x}\left[\frac{\sin x}{x}+\cos x \log x\right] \\$
$ =x^{\sin x-1} \sin x+x^{\sin x} \cos x \log x$
So, The correct option will be (B).