Derivative of Constant/Complex

Theorem
Let $\map {f_c} z$ be the constant function on an open domain $D \in \C$, where $c \in \C$.

Then:
 * $\forall z \in D : \map {f_c'} z = 0$

Proof
The function $f_c: D \to \C$ is defined as:
 * $\forall z \in D: \map {f_c} z = c$

Thus: