1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chapter 3 Review Limits and Continuity

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.1 Derivative of a Function

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

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

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Definition of Derivative

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Differentiable Function

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Definition of Derivative

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative at a Point (alternate)

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

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example One-sided Derivatives

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.2 Differentiability

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall How f’(a) Might Fail to Exist

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall How f’(a) Might Fail to Exist

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall How f’(a) Might Fail to Exist

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall How f’(a) Might Fail to Exist

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall How f’(a) Might Fail to Exist

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example How f’(a) Might Fail to Exist

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall How f’(a) Might Fail to Exist Most of the functions we encounter in calculus are differentiable wherever they are defined, which means they will not have corners, cusps, vertical tangent lines or points of discontinuity within their domains. Their graphs will be unbroken and smooth, with a well-defined slope at each point.

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Differentiability Implies Local Linearity A good way to think of differentiable functions is that they are locally linear; that is, a function that is differentiable at a closely resembles its own tangent line very close to a. In the jargon of graphing calculators, differentiable curves will “straighten out” when we zoom in on them at a point of differentiability.

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Differentiability Implies Local Linearity

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Differentiability Implies Continuity The converse of Theorem 1 is false. A continuous functions might have a corner, a cusp or a vertical tangent line, and hence not be differentiable at a given point.

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Intermediate Value Theorem for Derivatives Not every function can be a derivative.

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

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

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

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

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rule 1 Derivative of a Constant Function

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

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rule 3 The Constant Multiple Rule

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rule 4 The Sum and Difference Rule

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

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

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rule 5 The Product Rule

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Using the Product Rule

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rule 6 The Quotient Rule

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Using the Quotient Rule

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rule 7 Power Rule for Negative Integer Powers of x

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Negative Integer Powers of x

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Second and Higher Order Derivatives

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Second and Higher Order Derivatives

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

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

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.4 Velocity and Other Rates of Change

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Instantaneous Rates of Change

47. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Instantaneous Rates of Change

48. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Motion Along a Line

49. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Instantaneous Velocity

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

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

52. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Free-fall Constants (Earth)

53. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Finding Velocity

54. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Sensitivity to Change When a small change in x produces a large change in the value of a function f(x), we say that the function is relatively sensitive to changes in x. The derivative f’(x) is a measure of this sensitivity.

55. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivatives in Economics

56. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivatives in Economics

57. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

58. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

59. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.5 Derivatives of Trigonometric Functions

60. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of the Sine Function

61. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of the Cosine Function

62. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Finding the Derivative of the Sine and Cosine Functions

63. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Simple Harmonic Motion The motion of a weight bobbing up and down on the end of a string is an example of simple harmonic motion.

64. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Simple Harmonic Motion

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

66. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of the Other Basic Trigonometric Functions

67. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivative of the Other Basic Trigonometric Functions

68. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivative of the Other Basic Trigonometric Functions

69. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

70. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

71. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.6 Chain Rule

72. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rule 8 The Chain Rule

73. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivatives of Composite Functions

74. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall “Outside-Inside” Rule

75. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example “Outside-Inside” Rule

76. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Repeated Use of the Chain Rule

77. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Power Chain Rule

78. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

79. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

80. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

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

82. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Implicitly Defined Functions

83. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Implicitly Defined Functions

84. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Implicitly Defined Functions

85. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Implicit Differentiation Process

86. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivatives of a Higher Order

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

88. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

89. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

90. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.8 Derivatives of Inverse Trigonometric Functions

91. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivatives of Inverse Functions

92. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of the Arcsine

93. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivative of the Arcsine

94. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of the Arctangent

95. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of the Arcsecant

96. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivative of the Arcsecant

97. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Inverse Function – Inverse Cofunction Identities

98. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Calculator Conversion Identities

99. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivative of the Arccotangent

100. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

101. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Review Solutions

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

103. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of e x

104. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivative of e x

105. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of a x

106. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of ln x

107. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Derivative of ln x

108. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivative of log a x

109. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rule 10 Power Rule For Arbitrary Real Powers

110. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Power Rule For Arbitrary Real Powers

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

112. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Example Logarithmic Differentiation

113. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Quiz Sections 3.7 – 3.9

114. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Quiz Sections 3.7 – 3.9

115. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Quick Quiz Sections 3.7 – 3.9

116. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chapter Test Solutions

117. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chapter Test Solutions

118. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chapter Test Solutions