Sum rule of differentiation

The derivative of the sum is the sum of the derivatives.

Theorem (Sum Rule). Suppose

$f, g: {\bf R}^n \rightarrow {\bf R}^m$ are differentiable at $x = a$.

Then

$f + g: {\bf R}^n \rightarrow {\bf R}^m$ is differentiable at $x = a$ and $( f + g )'(a) = f'(a) + g'(a)$.