1. Derivative as slope of a tangent line
Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line)
2. Tangent slope example 1
The slope of a tangent line can be expressed as the limit of certain secant lines.
6. Slope of tangent line using derivative definition
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.
8. Tangent lines and rates of change
How tangent lines are a limit of secant lines, and where the derivative and rate of change fit into all this.
9. Formal and alternate form of the derivative
Compare different (equivalent) definitions for the derivative.
10. Formal and alternate form of the derivative for ln x
Enough abstract stuff already, let's see what the formal and alternative forms of the derivative look like in practice.
11. Formal and alternate form of the derivative example
A practice problem applying the different forms of the derivative.
12. The formal and alternate form of the derivative
Test your understanding of each definition of the derivative