Answer
$-e^{x}\sin e^{x}-\sin xe^{\cos x}$
Work Step by Step
$\dfrac {d}{dx}\left( e^{\cos x}+\cos \left( e^{x}\right) \right) =e^{\cos x}\times\left( \dfrac {d}{dx}\cos x\right) -\sin e^{x}\times \dfrac {d}{dx}\left( e^{x}\right) =-e^{x}\sin e^{x}-\sin xe^{\cos x}$
