If $f$ holomorphic in a domain $U$ and $f(z)\neq 0$ for all $z\in U$ then every zero of $f$ is such that $f(q)=0$ and $\det(Df_{p})>0$. Using that I have to prove that if $f$ keeps that conditions and $D$ is a disk such that $f(z)\neq 0$ for all $z\in \partial D$ then $\frac{1}{2i\pi }\int _{\partial D }\frac{df}{f}=$number of zeros of $f$ in $D$.
Now I have that $df=f'(z)dz$, so I have the expression $\frac{1}{2i\pi }\int _{\partial D }\frac{f'(z)}{f(z)}dz$.
But I don´t really know how that is useful, does any body can´t help? thanks for any help!