## Derivative Using the Limit Definition

We show, step-by-step, how to find the derivative of a function using the limit definition of derivative.

## Power Rule

We are now ready to look at the power rule for derivatives.  We will therefore begin by going through an example, followed by a proof that the rule we come up with will work in general.

## Dividing by zero: Imploding the Universe.

We can use this to show that every number is in fact equal to every other number, and the universe would implode into a single point.