A LevelMathsOCRMaths APureRevision NotesDifferentiationFurther DifferentiationProduct Rule

Product Rule (OCR A Level Maths A: Pure): Revision Note

Exam code: H240

Written by: Roger B

Reviewed by: Dan Finlay

Updated on 2 July 2026

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:

$\frac{d y}{d x} = u \frac{d v}{d x} + v \frac{d u}{d x}$

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:

$y' = u v' + v u'$

Product Rule Eg, AS & A Level Maths revision notes

Examiner Tips and Tricks

The product rule formulae are NOT in the formulae booklet – you need to know 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

Product Rule Prod Comp Illustr, AS & A Level Maths revision notes

To differentiate composite functions you need to use the chain rule

Worked Example

Product Rule Example, A Level & AS Level Pure Maths Revision Notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

I would just like to say a massive thank you for putting together such a brilliant, easy to use website.I really think using this site helped me secure my top gradesin science and maths. You really did save my exams! Thank you.

Beth
IGCSE Student

This website is soooo useful and I can’t ever thank you enough for organising questions by topic like this. Furthermore, the name of the website could not have been more appropriate as it literally did SAVE MY EXAMS!

Fathima
A Level Student

Incredible! SO worth my money, the revision notes have everything I need to know and are so easy to understand. I actually enjoy revising! It makes me feel a lot more confident for my GCSEs in a few months.

Kate
GCSE Student

Absolutely brilliant, both my girls used it for A levels and GCSE. It's saves on paper copies, also beneficial exam questions ranked from easy to hard. It's removed a lot of stress from the exams.

Sameera
Parent

Just to say that your resources are the best I have seen and I have been teaching chemistry at different levels for about 40 years

Mark
Chemistry Teacher

Excellent