Answer
$f'(x)=e^{x}(\cos x-\sin x)$
Work Step by Step
$f(x)=e^{x}\cos x$
Differentiate using the product rule:
$f'(x)=(e^{x})(\cos x)'+(\cos x)(e^{x})'=-e^{x}\sin x+e^{x}\cos x=...$
Take out common factor $e^{x}$ to obtain a better looking answer (Optional)
$...=e^{x}(\cos x-\sin x)$