1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rules for Differentiation Section 3.3

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 What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer Powers of x Second and Higher Order Derivatives … and why These rules help us find derivatives of functions analytically in a more efficient way.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 4 Rule 1 Derivative of a Constant Function

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 5 Rule 2 Power Rule for Positive Integer Powers of x.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 6 Rule 3 Power Rule for Negative Integer Powers of x

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 7 Rule 4 The Constant Multiple Rule

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 8 Rule 5 The Sum and Difference Rule

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 9 Example Positive Integer Powers, Multiples, Sums, and Differences

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 10 Example Positive Integer Powers, Multiples, Sums, and Differences

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 11 Example Negative Integer Powers of x

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Worksheet 3.3 Slide 3- 12

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 13 Rule 6 The Product Rule

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 14 Example Using the Product Rule

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 15 Rule 7 The Quotient Rule

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 16 Example Using the Quotient Rule

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 17 Second and Higher Order Derivatives

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 18 Second and Higher Order Derivatives

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Page 120 (11-19, 23-26, 33, 34) Slide 3- 19