# What is the derivative of  e^cosx + cos(e^x)?

$f ' = - {e}^{\cos x} \sin x - {e}^{x} \sin {e}^{x}$
$f ' = \left({e}^{\cos x} + \cos {e}^{x}\right) ' = {e}^{\cos x} \left(- \sin x\right) - \sin {e}^{x} \cdot {e}^{x}$
$f ' = - {e}^{\cos x} \sin x - {e}^{x} \sin {e}^{x}$