I am asked to prove that, supposing f is holomorphic on the region G, w $\in$ G and $\gamma$ is a positively oriented, simple, closed, smooth, G-contractiblecurve such that w is inside $\gamma$ , we know
$$f''(w)=\frac{1}{\pi i}\int_{\gamma } \frac{f(z)}{(z-w)^3} dz$$
I have very little idea on how to proceed, aside from that this is obviously an extension Cauchy's Integral Formula but I am not sure how to prove it, especially given that I have not previously been tasked with proving Cauchy's Integral formula in its conventional form. My very-basic-level intuition is to use the fact that if f is holomorphic on G then it is infinitely differentiable on G, but that feels backwards, like saying you can get out of a hole by going home and getting a ladder.
Thanks for any and all input