Quotient rule for derivatives

Theorem

Let $f$ and $g$ be differentiable functions with $g'(x) \neq 0$ for all $x$. Then the following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \left[ \dfrac{f(x)}{g(x)} \right] = \dfrac{g(x)f'(x)-f(x)g'(x)}{g(x)^2},$$ 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): $3.3.4$