Product Rule (Cambridge International A-Level Mathematics)

Product rule

What is the product rule?

• The product rule is a formula that allows you to differentiate a product of two functions
• If $y=u\times v$ where u and v are functions of x then the product rule is:

$\frac{dy}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}$

• In function notation, if $f(x)=g(x)\times h(x)$ then the product rule can be written as:

$f'(x)=g(x)h'(x)+h(x)g'(x)$

• The easiest way to remember the product rule is, for $y=u\times v$ where u and v are functions of x:

$y'=uv'+vu'$

Exam Hint

• The product rule formulae are in the formulae booklet – make sure you know how to find them.

• Don't confuse the product of two functions with a composite function:

  • The product of two functions is two functions multiplied together
  • A composite function is a function of a function

• To differentiate composite functions you need to use the chain rule

Worked Example