OCR A Level Maths: Pure

Revision Notes

A LevelMaths: PureOCRRevision Notes7. Differentiation7.2 Applications of Differentiation7.2.3 Second Order Derivatives

7.2.3 Second Order Derivatives

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Second Order Derivatives

What is the second order derivative of a function?

  • If you differentiate the derivative of a function (ie differentiate the function a second time) you get the second order derivative of the function
  • For a function y = f(x), there are two forms of notation for the second derivative (or second order derivative)

straight f to the power of apostrophe apostrophe end exponent left parenthesis x right parenthesis or fraction numerator d squared y over denominator d x squared end fraction

    • Note the positions of the power of 2's in the second version 

2nd Order Deriv Illustr 2, AS & A Level Maths revision notes

  • The second order derivative can also be referred to simply as the second derivative
    • Similarly, the 'regular' derivative can also be referred to as either the first order derivative or the first derivative
  • The second order derivative gives the rate of change of the gradient function (ie of the first derivative) – this will be important for identifying the nature of stationary points

Exam Tip

  • When finding second derivatives be especially careful with functions that have negative or fractional powers of x (see Worked Example below).
  • Mistakes made with fractions or negative signs can build up as you calculate the derivative more than once.

Worked example

2nd Order Deriv Example, A Level & AS Maths: Pure revision notes

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