## Kuvaus

## eMath 7: Derivatives

- 300-400 assignments + answers, in three levels of complexity
- Numerous example solutions
- Possibility to add comments and highlight text
- Possibility to check the correctness of the calculation

**Overview:** This book introduces the basic notions of calculus: continuity, limits, and derivatives. It shows how to compute the derivative of a function. It applies this to describe the behaviour of functions, and to find extreme values of functions. Additionally, it includes a chapter on how to work with rational expressions.

### Table of contents:

** 1 Preface**

**2 Rational Expressions**

2.1 Rational Expressions

2.2 Rational Equations

2.3 Rational Inequalities

**3 Continuity and Limits**

3.1 The Definition of Continuity and Limit

3.2 Calculating Limits

3.3 Piecewise Defined Functions

3.4 Results Related to Continuous Functions

**4 Derivative**

4.1 Derivative And Difference Quotient

4.2 Differentiation Rules

4.3 Tangents and Normals

**5 The Behavior of a Function**

5.1 The Monotonicity of a Function

5.2 Derivative and Monotonicity

5.3 Local Extreme Values

5.4 The Greatest and Smallest Value of a Function