I am working on this question and its "simplicity" is sort of throwing me off.
"Assume that the series $\sum_{n = -\infty}^{\infty} a_n(z − z_0)^n$ converges in $A_{r,R} (z_0)$ with $0 \leq r < R$. Define the function \begin{equation} f(z) = \sum_{n = -\infty}^{\infty} a_n(z − z_0)^n. \end{equation} Show that $f(z)$ is differentiable for $z \in A_{r,R} (z_0)$ and calculate the differential."
Do I need to split the Laurent series into both its regular and singular parts as they both converge?