# 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 $\map {f'} z$:
$\ds \forall z \in D : \map {f'} z := \lim_{h \mathop \to 0} \frac {\map f {z + h} - \map f z} h$