Differentiation rules > Quotient rule
123456Quotient rule

## Theory

To find the derivative of the quotient of two functions you use

Differentation rule 7 (quotient rule):
If $Q\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$ (with g(x) ≠ 0) then $Q\text{'}\left(x\right)=\frac{f\text{'}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g\text{'}\left(x\right)}{{\left(g\left(x\right)\right)}^{2}}$.

Function $f$ is the numerator of the fraction, function $g$ is the denominator of the fraction.

You may not always need this differentiation rule. Sometimes you can simplify a quotient.
This rule is often used in combination with the previous differentiation rules.
Especially in combination with the chain rule!