Contents

**Chapter 1 Rates of Change and the Derivative**
1.1 Average Rates of Change

1.1.1 Exercises

1.2 Prelude to IROC's

1.2.1 Exercises

1.3 Limits and Continuity

1.3.1 Limits

1.3.2 Continuous Functions

1.3.3 Limits involving Infinity

1.3.4 Exercises

1.4 IROC's and the Derivative

1.4.1 Exercises

1.5 Extrema and the Mean Value Theorem

1.5.1 Exercises

1.6 Higher-Order Derivatives

1.6.1 Exercises

Appendix 1.A Technical Matters

1.A.1 Properties of Real Numbers and Extended Real Numbers

1.A.2 Functions

1.A.3 Proofs of Theorems on Limits and Continuity

1.A.4 Proofs of Theorems on Differentiability and Continuity

**Chapter 2 Basic Rules for Calculating Derivatives **
2.1 The Power Rule and Linearity

2.1.1 Exercises

2.2 The Product and Quotient Rules

2.2.1 Exercises

2.3 The Chain Rule and Inverse Functions

2.3.1 Exercises

2.4 The Exponential Function

2.4.1 Exercises

2.5 The Natural Logarithm

2.5.1 Exercises

2.6 General Exponential and Logarithmic Functions

2.6.1 Exercises

2.7 Trigonometric Functions: Sine and Cosine

2.7.1 Exercises

2.8 The Other Trigonometric Functions

2.8.1 Exercises

2.9 Inverse Trig Functions

2.9.1 Exercises

2.10 Implicit Functions

2.10.1 Exercises

Appendix 2.A Technical Matters

**Chapter 3 Applications of Differentiation**
3.1 Related Rates

3.1.1 Exercises

3.2 Graphing

3.2.1 Exercises

3.3 Optimization

3.3.1 Exercises

3.4 Linear Approximation

3.4.1 Exercises

3.5 l'Hôpital's Rule

3.5.1 Exercises

Appendix 3.A Technical Matters

Chapter 4 Anti-differentiation & Differential Equations

4.1 What is a Differential Equation?

4.1.1 Exercises

4.2 Anti-derivatives

4.2.1 Exercises

4.3 Separable Differential Equations

4.3.1 Exercises

4.4 Applications of Differential Equations

4.4.1 Exercises

4.5 Approximating Solutions

4.5.1 Exercises

Appendix A Parameterized Curves and Motion

A.1 Parameterized Curves

A.1.1 Exercises

Appendix B Tables of Derivative Formulas

Appendix C Answers to Odd-Numbered Problems