Product rule for derivatives

Theorem

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.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $3.3.3$