Derivative of Constant Multiple

Theorem
Let $f$ be a real function which is differentiable on $\R$.

Let $g$ be a complex function which is complex-differentiable at all points in $D$ where $D \subseteq \C$.

Let $c \in \R$ and $d \in D$ be a constant.

Then:
 * $D_x \left({c f \left({x}\right)}\right) = c D_x \left({f \left({x}\right)}\right)$
 * $\forall z \in D : D_z \left({d g \left({z}\right)}\right) = d D_z \left({g \left({z}\right)}\right)$