# Ch 13: Introduction to the Derivative

### About This Chapter

## Introduction to the Derivative - Chapter Summary and Learning Objectives

The lessons in this chapter can give you a basic understanding of derivatives and the rate of change. You'll learn how velocity, or the rate of change, is affected by the changes of another variable. These lessons will also teach you how the rate of change can be graphed as a slope. You will be introduced to the formal definition of a derivative and shown how to write derivative equations. This chapter includes video lessons that are designed to teach you the following:

- How the rate of change is altered by variables
- The relationship between rate of change and slopes
- How to determine the rate of change from a graph
- How to graph the rate of change
- How to determine the tangent on a curve
- The formal definition of derivatives and how they are used
- How to write derivatives

Video | Objective |
---|---|

Velocity and the Rate of Change | Understand how velocity is the rate of change in a derivative. Review what types of variables can affect the rate of change and how to graph an inconsistent slope. |

Slopes and the Rate of Change | Learn how to depict the rate of change on a graph. This lesson covers how the slope is affected by the rate of change and how to identify the tangent on a curve. |

Derivatives: The Formal Definition | Define derivatives and learn how they are related to the rate of change. See how to write equations for derivatives using different variables. |

### 1. Velocity and the Rate of Change

Running from your little sister or just window-shopping, your speed is just a measure of how fast you move, or how your position is changing over time. In this lesson, learn about how velocity is a rate of change.

### 2. Slopes and Rate of Change

If you throw a ball straight up, there will be a point when it stops moving for an instant before coming back down. Consider this as we study the rate of change of human cannonballs in this lesson.

### 3. Derivatives: The Formal Definition

The derivative defines calculus. In this lesson, learn how the derivative is related to the instantaneous rate of change with Super C, the cannonball man.

### 4. Graphing the Derivative from Any Function

When you know the rules, calculating the derivates of equations is relatively straightforward, although it can be tedious! What happens, though, when you don't know the function? In this lesson, learn how to graph the derivative of a function based solely on a graph of the function!

### 5. Calculating Derivatives of Polynomial Equations

Polynomials can describe just about anything and are especially common in describing motion. Learn the tricks to quickly finding the derivatives of these ubiquitous functions.

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### Other Chapters

Other chapters within the Math 105: Precalculus Algebra course

- Mathematical Modeling
- Linear Equations & Inequalities
- Quadratic Functions
- Rational Expressions and Functions
- Polynomial Functions of a Higher Degree
- Absolute Value Equations & Inequalities
- Complex Numbers
- Geometry Basics
- Functions Overview
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Studying for Math 105