Definition:Derivative/Complex Function/Open Set

Definition
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 $f' \left({z}\right)$:
 * $\displaystyle \forall z \in D : f' \left({z}\right) := \lim_{h \mathop \to 0} \frac {f \left({z + h}\right) - f \left({z}\right)} h$