This section of the Crash Course explains what Limits are and why they are useful. Shini (the woman in the video) explains what an interval is and how they are used for limits.

This video explains the main focus of derivatives. This Crash Course Narrator, Shini, defines how to use mathematics to write derivatives and calculate them. Additionally, Shini introduces the Power Rule (which is a way to calculate derivatives)

The team at NASA is trying to launch a capsule and bring it back to Earth. To do so, they need to calculate its change in trajectory as it moves from an elliptical orbit to a parabolical orbit. Katherine discovers that they can use Euler's Method to approximate the change in trajectory.

Bart's gifted school teacher hides a joke in the answer of a derivatives problem. Bart doesn't seem to get the joke, so the teacher briefly explains how she arrived at the answer.

This Crash Course video gives different explanations of derivatives. She iterates how to use the power rule with negative exponents as well as fractions.