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JEE Math Practice Question

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:

  1. A.4
  2. B.5
  3. C.3
  4. D.8

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