Quotient Rule (Edexcel IAL Maths)

Spec point — 4.2

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:

$\frac{dy}{dx}=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^{2}}$

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

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

Exam Hint

• 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