1. Chapter 3
Derivatives

2. Introducing the Derivative
3.1
Introducing the Derivative

3. Figure 3.1

4. Figure 3.2

5. Figure 3.3

6. Figure 3.4

8. Figure 3.5

9. Figure 3.6

11. Figure 3.7

12. Figure 3.8

14. Figure 3.9

15. Figure 3.10

16. Figure 3.11

17. Working with Derivatives
3.2
Working with Derivatives

18. Figure 3.12

19. Figure 3.13

20. Figure 3.14

21. Figure 3.15

22. Figure 3.16

23. Figure 3.17

25. Figure 3.18

27. Figure 3.19

28. Figure 3.20 (a)

29. Figure 3.20 (b)

31. Figure 3.21

32. Figure 3.22

33. Rules of Differentiation
3.3
Rules of Differentiation

34. Figure 3.23

39. Table 3.1

40. Figure 3.24

41. Figure 3.25

44. Figure 3.26

45. Figure 3.27

47. The Product and Quotient Rules
3.4
The Product and Quotient Rules

50. Figure 3.28

53. Figure 3.29

54. Derivatives of Trigonometric Functions
3.5
Derivatives of
Trigonometric Functions

56. Table 3.2

57. Figure 3.30

58. Figure 3.31

60. Figure 3.32 (a & b)

62. Derivatives as Rates of Change
3.6
Derivatives as Rates of Change

63. Figure 3.33

64. Figure 3.34

66. Figure 3.35

67. Figure 3.36

69. Figure 3.37

70. Figure 3.38

71. Figure 3.39

72. Figure 3.40 (a)

73. Figure 3.40 (b)

74. Figure 3.41

75. Figure 3.42

76. Figure 3.43

77. Figure 3.44

78. Figure 3.45

80. Figure 3.46

81. Figure 3.47 (a)

82. Figure 3.47 (b)

83. Figure 3.48

85. Figure 3.49

86. 3.7
The Chain Rule

87. Figure 3.50

90. Table 3.3

91. Table 3.4

92. Table 3.5

94. Figure 3.51

95. Implicit Differentiation
3.8
Implicit Differentiation

96. Figure 3.52 (a & b)

97. Figure 3.53 (a)

98. Figure 3.53 (b)

99. Figure 3.54

100. Figure 3.55

102. Figure 3.56

103. Derivatives of Logarithmic and Exponential Functions
3.9
Derivatives of Logarithmic
and Exponential Functions

104. Figure 3.57

106. Figure 3.58 (a & b)

108. Figure 3.59

110. Table 3.6
Source: E.G. Hook and A. Lindsjo, Down Syndrome in Live Births by Single Year Maternal Age.

111. Figure 3.60

113. Figure 3.61

115. Derivatives of Inverse Trigonometric Functions
3.10
Derivatives of Inverse
Trigonometric Functions

116. Figure 3.62

117. Figure 3.63

119. Figure 3.64

120. Figure 3.65

121. Figure 3.66

123. Figure 3.67

124. Figure 3.68

125. Figure 3.69

126. Figure 3.70

128. Figure 3.71

129. 3.11
Related Rates

130. Figure 3.72

132. Figure 3.73

133. Figure 3.74

134. Figure 3.75

135. Figure 3.76