Suppose for a differentiable function $h, h(0)=0, h(1)=1$ and $h^{\prime}(0)=h^{\prime}(1)=2$. If $g (x)=h\left( e ^x\right) e ^{h(x)}$, then $g^{\prime}(0)$ is equal to : [JEE Main 2024, 6 Apr (Shift 2)]

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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( e …

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