Product rule for derivatives

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Theorem[edit]

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

Proof[edit]

References[edit]