Differentiation

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