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