Combination Theorem for Complex Derivatives

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

Let $f, g: D \to \C$ be complex-differentiable functions on $D$

Let $z \in D$.

Let $w, c \in \C$ be arbitrary complex numbers.

Then the following results hold:

Also see

 * Sum Rule for Derivatives
 * Derivative of Constant Multiple
 * Product Rule for Derivatives
 * Quotient Rule for Derivatives

These theorems show that identical results hold for derivatives of real functions.