# Introduction to derivatives

1 article

9 videos

2 skills

Discover what magic we can derive when we take a derivative, which is the slope of the tangent line at any point on a curve.

### Derivative as slope of a tangent line

VIDEO
15:43 minutes

Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line)

### Tangent slope example 1

VIDEO
5:25 minutes

The slope of a tangent line can be expressed as the limit of certain secant lines.

### Tangent slope example 2

VIDEO
6:05 minutes

### Tangent slope example 3

VIDEO
3:46 minutes

### Tangent slope

PRACTICE PROBLEMS

Test your understanding of a tangent line as the limit of secant slopes.

### Slope of tangent line using derivative definition

VIDEO
8:28 minutes

The derivative can be thought of the slope of a tangent line, which is defined as the limit of the slopes of certain secant lines. See what this looks like in action.

### The derivative of f(x)=x^2 for any x

VIDEO
11:05 minutes

Here we find a formula for the derivative of f(x)=x^2.

### Tangent lines and rates of change

ARTICLE

How tangent lines are a limit of secant lines, and where the derivative and rate of change fit into all this.

### Formal and alternate form of the derivative

VIDEO
4:53 minutes

Compare different (equivalent) definitions for the derivative.

### Formal and alternate form of the derivative for ln x

VIDEO
5:46 minutes

Enough abstract stuff already, let's see what the formal and alternative forms of the derivative look like in practice.

### Formal and alternate form of the derivative example

VIDEO
5:17 minutes

A practice problem applying the different forms of the derivative.

### The formal and alternate form of the derivative

PRACTICE PROBLEMS

Test your understanding of each definition of the derivative