International A LevelMaths: Pure 3EdexcelRevision Notes4. Differentiation4.1 Further Differentiation4.1.3 Product Rule

Product Rule (Edexcel International A Level Maths: Pure 3)

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Roger

Last updated

28 April 2023

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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 Tip

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

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Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.