解答

$${y=e^x(\cos x+\sin x)}$$

$$\begin{eqnarray*} y'&=&\left(e^x\right)'(\cos x+\sin x) +e^x(\cos x+\sin x)'\\ &=& e^x(\cos x+\sin x)+e^x(-\sin x+\cos x)\\ &=& 2e^x\cos x \end{eqnarray*}$$