Contents
Preface
vii
1 Understanding the Derivative
1
1.1 How do we measure velocity? . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2 The notion of limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 The derivative of a function at a point . . . . . . . . . . . . . . . . . . . . 22
1.4 The derivative function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5 Interpreting, estimating, and using the derivative . . . . . . . . . . . . . . 43
1.6 The second derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1.7 Limits, Continuity, and Differentiability . . . . . . . . . . . . . . . . . . . . 65
1.8 The Tangent Line Approximation . . . . . . . . . . . . . . . . . . . . . . . 77
2 Computing Derivatives
87
2.1 Elementary derivative rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.2 The sine and cosine functions . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.3 The product and quotient rules . . . . . . . . . . . . . . . . . . . . . . . . 102
2.4 Derivatives of other trigonometric functions . . . . . . . . . . . . . . . . . 113
2.5 The chain rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
2.6 Derivatives of Inverse Functions . . . . . . . . . . . . . . . . . . . . . . . . 129
2.7 Derivatives of Functions Given Implicitly . . . . . . . . . . . . . . . . . . . 140
2.8 Using Derivatives to Evaluate Limits . . . . . . . . . . . . . . . . . . . . . . 149
3 Using Derivatives
161
3.1 Using derivatives to identify extreme values . . . . . . . . . . . . . . . . . 161
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