1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Product and Quotient Rules for Differentiation

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 2 Quick Review Find the limits: 1.4. 2.5. 3.6.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review - Solutions 1. 4. 2. 5. 3. 6. Slide 3- 3

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 4 What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Second and Higher Order Derivatives … and why These rules help us find derivatives of functions analytically in a more efficient way.

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

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 6 Power Rule Trigonometric Rules

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 7 Examples Find the derivative of the following functions: 1. 2. 3. 4.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 8 Examples - Solutions Find the derivative of the following functions: 1. 2. 3. 4.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 9 Example Horizontal Tangents A horizontal tangent is where is the slope of the tangent line is equal to 0,

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

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 11 The Product Rule

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 12 Example Using the Product Rule

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

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

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 15 Example: Finding the Slope of a Graph 1.Find the slope of the graph at the point 2.Find the slope of the graph at the point

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 16 Example: Finding the Equation of a Tangent Line 1.Find the equation of the tangent line to the graph at the point 2.Find the equation of the tangent line to the graph at the point

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 Slide 3- 19 Quick Quiz Sections 2.1 – 2.3

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 20 Quick Quiz Sections 2.1 – 2.3

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 21 Quick Quiz Sections 2.1 – 2.3

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 22 Quick Quiz Sections 2.1 – 2.3

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 23 Quick Quiz Sections 2.1 – 2.3

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 24 Quick Quiz Sections 2.1 – 2.3