Sum Rule for Derivatives

Theorem
Let $$f \left({x}\right), j \left({x}\right), k \left({x}\right)$$ be continuous real functions.

Let $$f \left({x}\right) = j \left({x}\right) + k \left({x}\right)$$.

Then $$\frac{d}{dx} f \left({x}\right) = \frac{d}{dx} j \left({x}\right) + \frac{d}{dx} k \left({x}\right)$$.

Proof
$$ $$ $$ $$ $$ $$ $$

Q.E.D.