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

Category: A-level课程, 教材笔记, 福利干货 Date: 2022年8月8日下午5:45

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Derivatives of Exponential Functions

What is the derivative of e?

y = e^x has the particular property

ie for every real number x, the gradient of y = e^x is also equal to e^x(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

转载自savemyexams

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