\begin{definition}[Definition:Derivative/Complex Function/Open Set]
Let $D\subseteq \C$ be an open set.
Let $f : D \to \C$ be a complex function.
Let $f$ be complex-differentiable in $D$.
Then the '''derivative of $f$''' is the complex function  $f': D \to \C$ whose value at each point $z \in D$ is the derivative $\map {f'} z$:
:$\ds \forall z \in D : \map {f'} z := \lim_{h \mathop \to 0} \frac {\map f {z + h} - \map f z} h$
Category:Definitions/Complex Analysis
\end{definition}