Answer
$$ f'(x)= \cos x e^{\sin x}.$$
Work Step by Step
Recall that $(e^x)'=e^x$
Recall that $(\sin x)'=\cos x$.
Since we have
$$ f(x)= e^{\sin x}$$
then the derivative $ f'(x)$, using the chain rule, is given by
$$ f'(x)= e^{\sin x}\left(\sin x\right)'=\cos x e^{\sin x}.$$
