#math/calculus For differentiable functions $f,g$ with $g(x)\neq 0$, the **quotient rule** is $ \left(\frac{f}{g}\right)'(x) =\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^{2}}. $ It follows by writing $f/g=f\cdot(1/g)$ and applying the [[1B2 - Product Rule|product rule]] with the [[1B4 - Reciprocal Rule|reciprocal rule]]. > [!Mnemonic] > “Derivative of the numerator times the denominator, minus the numerator times the derivative of the denominator, over the denominator squared.” Setting $g=1$ is a quick sign check: the result must reduce to $f'$.