Assume that $f_n,f:D(0,1)\rightarrow C$ are holomorphic. and $f_n \rightarrow f$ uniformly on every compact set. we need to show that $f'_n \rightarrow f'$ uniformly on every compact set.
I kind of have no idea how to approach this one, its from a test I attended and I'm going for a second go at it and I want to understand the first one, first.