Use L' Hopital's Rule to find the limit of f(x) at x=0 first.

f(x) = g(x)/x, since g is a differentiable function,

therefore f(x) must be differentiable somewhere on R.

assume f'(x) exists at point x=k, then

f'(k) = [k g'(k) - g(k) ]/k^2. (by quotient rule)

take above expression become a limit which k approach 0 and apply L' Hopital's Rule to show that f is differentiable at x=0, and hence find f'(0), the answer should be 7.