Let $\displaystyle z_0$ be an isolated point of a function $\displaystyle f$ and suppose that $\displaystyle f(z)=\frac{\phi(z)}{(z-z_0)^m}$, where $\displaystyle m$ is a positive integer and $\displaystyle \phi(z)$ is analytic and nonzero at $\displaystyle z_0$. By applying the extended form of the Cauchy integral formula to the function $\displaystyle \phi(z)$, show that $\displaystyle \text{Res}_{z=z_0}=\frac{\phi^{(m-1)}(z_0)}{(m-1)!}$.

I do not see how to do this. Our book says:

Since there is a neighborhood $\displaystyle |z-z_0|< \epsilon$ throughout which $\displaystyle \phi(z)$ is analytic, the contour used in the extended Cauchy integral formula can be the positively oriented circle $\displaystyle |z-z_0|< \frac{\epsilon}{2}$. How do I use this suggestion? I don't see that now. Thanks in advance.