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Derivatives of Exponential Functions (Cambridge (CIE) AS Maths) : Revision Note

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Cambridge (CIE) Maths: Pure 2AQA Maths: PureOCR Maths A: PureEdexcel Maths: Pure

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Derivatives of Exponential Functions

What is the derivative of e?

  • y = ex has the particular property

fraction numerator d y over denominator d x end fraction italic equals e to the power of x

  • ie for every real number x, the gradient of y = ex is also equal to ex (see Derivatives of Exponential Functions)

Derivatives of Exponential Functions Notes fig1, A Level & AS Maths: Pure revision notes

 

Derivatives of Exponential Functions Notes fig2, A Level & AS Maths: Pure revision notes

 

  • e ≈ 2.718 (see "e")

  • Recall that the derivative is the gradient function for a curve (see First Principles Differentiation)

Derivatives of Exponential Functions Notes fig3, A Level & AS Maths: Pure revision notes

  •  The derivative of y = ekx is

    • fraction numerator d y over denominator d x end fraction italic equals k e to the power of k x end exponent

  • The derivative of y = e-kx is

    • fraction numerator d y over denominator d x end fraction italic equals italic minus k e to the power of negative k x end exponent

Examiner Tips and Tricks

  • Remember that (like π) e is a number.

  • Exam questions can ask for answers to be given as exact values in terms of e (see the Worked Example below).

Worked Example

Derivatives of Exponential Functions Example fig1, A Level & AS Maths: Pure revision notes
Derivatives of Exponential Functions Example fig2, A Level & AS Maths: Pure revision notes
Derivatives of Exponential Functions Example fig3, A Level & AS Maths: Pure revision notes
Derivatives of Exponential Functions Example fig4, A Level & AS Maths: Pure revision notes
Derivatives of Exponential Functions Example fig5, A Level & AS Maths: Pure revision notes

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    Paul

    Author: Paul

    Expertise: Maths Content Creator (Previous)

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams.