Suppose for a differentiable function h, h(0)=0, h(1)=1 and h^′(0)=h^′(1)=2. If g(x)=h(e^x) e^h(x), then g^′(0) is equal to:

Suppose for a differentiable function $\displaystyle h, h(0)=0, h(1)=1$ and $\displaystyle h^{\prime}(0)=h^{\prime}(1)=2$. If $\displaystyle g(x)=h\left(e^x\right) e^{h(x)}$, then $\displaystyle \mathrm{g}^{\prime}(0)$ is equal to: