Question of the Day

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The functions $h(x)$ and $g(x)$ are differentiable such that the derivative of $h$ is $h$ and the derivative of $g$ is $g$ . That is $h'(x)=h(x)$ and $g'(x)=g(x)$ , also, the function $h(x)$ is non-zero for all $x$ . Prove that $g(x) = k h(x)$ for some constant $k$ .