Derivative of Constant Multiple/Complex

Theorem
Let $D$ be an open subset of the set of complex numbers $\C$.

Let $f: D \to \C$ be a complex-differentiable function on $D$.

Let $c \in \C$ be a constant.

Then:
 * $\forall z \in D : \map {D_z} {c \map f z} = c \map {D_z} {\map f z}$