Sum rule for derivatives

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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.

Proof

References