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A LevelMaths: PureOCRRevision Notes7. Differentiation7.4 Further Applications of Differentiation7.4.3 Connected Rates of Change

Connected Rates of Change (OCR A Level Maths: Pure)

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Connected Rates of Change

What are connected rates of change?

  • In situations involving more than two variables you can use the chain rule to connect multiple rates of change into a single equation

Conn Rates of Ch Illustr 1, AS & A Level Maths revision notes

  • Equations involving derivatives (ie rates of changes) are known as differential equations
    • These can be solved using methods of integration (see Differential Equations )
    • However setting up the equation from the information given can involve the chain rule and connected rates of change

    Conn Rates of Ch Illustr 2, AS & A Level Maths revision notes 

  • Note from the examples above that you will often need to differentiate a formula to get one of the rates of change you need

Examiner Tip

  • These problems can involve a lot of letters – be sure to keep track of what they all refer to.
  • Be especially sure that you are clear about which letters are variables and which are constants – these behave very differently when differentiation is involved!

Worked example

Conn Rates of Ch 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.