Question of the Day By Maths Grinds

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 $k$.