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AQA A Level Maths: Pure復(fù)習(xí)筆記6.1.4 Derivatives of Exponential Functions

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月8日 下午5:45

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?ex?(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?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

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

 

 

 

 

 

 

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