Suppose f is differentiable. Prove that

$\displaystyle f'(x)=\lim_{h\to 0}\frac{f(x+g(h))-f(x)}{g(h)}$ exists, where g is a nonzero function of h such that $\displaystyle \lim_{h\to 0}g(h)=0$ and find the value of $\displaystyle f'(x)$.

I think I need to change the terms of the limit from h to g(h) going to zero, not sure how to though.

Any thoughts?