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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.9 Derivatives of Exponential and Logarithmic Functions.

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Presentation on theme: "Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.9 Derivatives of Exponential and Logarithmic Functions."— Presentation transcript:

1 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.9 Derivatives of Exponential and Logarithmic Functions

2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 2 Quick Review

3 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 3 Quick Review

4 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall

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6 Slide 3- 6 Quick Review Solutions

7 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 7 Quick Review Solutions

8 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall

9 Slide 3- 9 What you’ll learn about Derivative of e x Derivative of a x Derivative of ln x Derivative of log a x Power Rule for Arbitrary Real Powers … and why The relationship between exponential and logarithmic functions provides a powerful differentiation tool called logarithmic differentiation.

10 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 10 Derivative of e x

11 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 11 Example Derivative of e x

12 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 12

13 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 13

14 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 14 Derivative of a x

15 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 15

16 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 16

17 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Assignment 3.9.1 pages 178 – 179, # 1 – 9 odds, 29, 33, 49, 51 and 55 Slide 3- 17

18 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 18 Derivative of ln x

19 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 19 Example Derivative of ln x

20 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 20 Derivative of log a x

21 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 21 Rule 10 Power Rule For Arbitrary Real Powers

22 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 22 Example Power Rule For Arbitrary Real Powers

23 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 23 Logarithmic Differentiation Sometimes the properties of logarithms can be used to simplify the differentiation process, even if logarithms themselves must be introduced as a step in the process. The process of introducing logarithms before differentiating is called logarithmic differentiation.

24 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 24 Example Logarithmic Differentiation

25 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall

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34 Slide 3- 34 Quick Quiz Sections 3.7 – 3.9

35 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 35 Quick Quiz Sections 3.7 – 3.9

36 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 36 Quick Quiz Sections 3.7 – 3.9

37 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 37 Quick Quiz Sections 3.7 – 3.9

38 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 38 Quick Quiz Sections 3.7 – 3.9

39 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 39 Quick Quiz Sections 3.7 – 3.9

40 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Assignment 3.9.2 pages 178 – 180, # 11 – 27odds, 31,37, 39, 41, 56 and 64 Slide 3- 40


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