1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.7 Implicit Differentiation

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 2 Quick Quiz Sections 3.4 – 3.6

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 3 Quick Quiz Sections 3.4 – 3.6

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 4 Quick Quiz Sections 3.4 – 3.6

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 5 Quick Quiz Sections 3.4 – 3.6

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 6 Quick Quiz Sections 3.4 – 3.6

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 7 Quick Quiz Sections 3.4 – 3.6

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 8 What you’ll learn about Implicitly Defined Functions Lenses, Tangents, and Normal Lines Derivatives of Higher Order Rational Powers of Differentiable Functions … and why Implicit differentiation allows us to find derivatives of functions that are not defined or written explicitly as a function of a single variable.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 9 Implicitly Defined Functions

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

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 11 Implicit Differentiation Process

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

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

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Find dy / dx Slide 3- 14

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

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Find dy / dx and the slope if the curve at the indicated point. Slide 3- 16

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 17 Lenses, Tangents and Normal Lines In the law that describes how light changes direction as it enters a lens, the important angles are the angles the light makes with the line perpendicular to the surface of the lens at the point of entry (angles A and B in Figure 3.50). This line is called the normal to the surface at the point of entry. In a profile view of a lens, the normal is a line perpendicular to the tangent to the profile curve at the point of entry. Implicit differentiation is often used to find the tangents and normals of lenses described as quadratic curves.

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 18 Lenses, Tangents and Normal Lines

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 19 Example Lenses, Tangents and Normal Lines

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

22. Slide 3- 22 Example Lenses, Tangents and Normal Lines

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 23 Example Lenses, Tangents and Normal Lines

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Assignment 3.7.1 page 162, # 3 – 24 multiples of 3 Slide 3- 24

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 25 Example Derivatives of a Higher Order

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

28. Slide 3- 28

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

32. Slide 3- 32

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 33 Rule 9 Power Rule For Rational Powers of x

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 34

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 35

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 36

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Find equations for the tangent and normal to the cissoid of Diocles at the point (1,1). Slide 3- 37

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Explain how to produce the graph of the cissoid of Diocles on a graphing calculator. Slide 3- 38

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Find the slope of the folium of Descartes, x 3 + y 3 -9xy = 0, at the points (4,2) and (2,4). Slide 3- 39

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall At what point (other than the origin) does the folium of Descartes, x 3 + y 3 -9xy = 0, have a horizontal tangent? Slide 3- 40

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 41 Quick Review

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 42 Quick Review

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 43 Quick Review

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 44 Quick Review Solutions

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 45 Quick Review Solutions

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 46 Quick Review Solutions

47. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Assignment 3.7.2 pages 162 – 164, 27 – 48 multiples of 3, 54 and 58 Slide 3- 47