Differentiation rules > Quotient rule

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!