AQA A Level Maths: Pure复习笔记6.1.4 Derivatives of Exponential Functions

Derivatives of Exponential Functions

What is the derivative of e?

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

6.1.4-Derivatives-of-Exponential-Functions-Notes-fig1

6.1.4-Derivatives-of-Exponential-Functions-Notes-fig2

  • e ≈ 2.718 (see "e")
  • Recall that the derivative is the gradient function for a curve (see First Principles Differentiation)

Graphs and derivatives related to e

6.1.4-Derivatives-of-Exponential-Functions-Notes-fig3

  • Exam Tip
  • Remember that (like πe 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

6.1.4-Derivatives-of-Exponential-Functions-Example-fig1

6.1.4-Derivatives-of-Exponential-Functions-Example-fig2

6.1.4-Derivatives-of-Exponential-Functions-Example-fig3

6.1.4-Derivatives-of-Exponential-Functions-Example-fig4

6.1.4-Derivatives-of-Exponential-Functions-Example-fig5

 

 

 

 

 

 

转载自savemyexams

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