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A LevelMaths: PureAQARevision Notes7. Differentiation7.3 Further Differentiation7.3.4 Product Rule

Product Rule (AQA A Level Maths: Pure)

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Roger

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Roger

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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 bold italic y bold equals bold italic u bold cross times bold italic v where u and v are functions of x then the product rule is:
fraction numerator d y over denominator d x end fraction equals u fraction numerator d v over denominator d x end fraction plus v fraction numerator d u over denominator d x end fraction

  • In function notation, if bold f bold left parenthesis bold italic x bold right parenthesis bold equals bold g bold left parenthesis bold italic x bold right parenthesis bold cross times bold h bold left parenthesis bold italic x bold right parenthesis then the product rule can be written as:
straight f apostrophe left parenthesis x right parenthesis equals straight g left parenthesis x right parenthesis straight h apostrophe left parenthesis x right parenthesis plus straight h left parenthesis x right parenthesis straight g apostrophe left parenthesis x right parenthesis
  • The easiest way to remember the product rule is, for bold italic y bold equals bold italic u bold cross times bold italic v where u and v are functions of x:
y apostrophe space equals space u v apostrophe space plus space v u apostrophe
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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    Roger

    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.