ASMathsCambridge (CIE)Pure 2Revision NotesDifferentiationFurther DifferentiationProduct Rule

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

Exam code: 9709

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 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

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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