Sum rule for derivatives

Theorem

Let $f$ and $g$ be differentiable functions. Then, $$\dfrac{\mathrm{d}}{\mathrm{d}x}[f(x)+g(x)] = f'(x)+g'(x),$$ where $\dfrac{\mathrm{d}}{\mathrm{d}x}$ denotes the derivative operator.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $3.3.2$