ASMathsCambridge (CIE)Pure 2Revision NotesDifferentiationFurther DifferentiationQuotient Rule

Quotient Rule (Cambridge (CIE) AS Maths: Pure 2): Revision Note

Exam code: 9709

Written by: Roger B

Reviewed by: Dan Finlay

Updated on 2 July 2026

Quotient rule

What is the quotient rule?

The quotient rule is a formula that allows you to differentiate a quotient of two functions (ie one function divided by another)
If $y = \frac{u}{v}$ where u and v are functions of x then the quotient rule is:

$\frac{d y}{d x} = \frac{v \frac{d u}{d x} - u \frac{d v}{d x}}{v^{2}}$

In function notation, if $f (x) = \frac{g (x)}{h (x)}$ then the quotient rule can be written as:

$f' (x) = \frac{h (x) g' (x) - g (x) h' (x)}{(h {(x))}^{2}}$

Quotient Rule Eg, AS & A Level Maths revision notes

Examiner Tips and Tricks

The quotient rule formula is in the formulae booklet – you don't have to memorise it.
Be careful using the formula – because of the minus sign in the numerator the order of the functions is important.
Look out for functions of the form $f (x) = g (x) {(h (x))}^{- 1}$
- You could differentiate that using a combination of the chain rule and the product rule (and it can be good practice for you to try it!)
- But it can also be seen as just a quotient rule question in disguise
  - $g (x) {(h (x))}^{- 1} = \frac{g (x)}{h (x)}$

Worked Example

Quotient Rule Example, AS & A Level Maths revision notes

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