Derivative of Constant/Complex

Theorem
Let $f_c \left({z}\right)$ be the constant function on a domain $D \in \C$, where $c \in D$.

Then $\forall z \in D : f_c' \left({z}\right) = 0$.

Proof
The function $f_c: D \to D$ is defined as $\forall z \in D: f_c \left({z}\right) = c$.

Thus: