eMath 7 Derivatives (OPS03)



eMath 7: Derivatives

The e-book is structured so that you will learn all concepts in a logical order and it is meant to be studied from beginning to end. The theory parts are short and concise and at the end of each lesson, you will find a page with assignments. The assignments can be solved directly in the book. You can easily write mathematics on the computer with the eMathStudio math tools, as well as insert pictures, embedded elements and graphs to support your studies and solutions.
Each eMath book includes:
  • 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