The Limit Definition of The Derivative

So we learned that the derivative of a function at a point is the slope of the line tangent to the graph of the function at that point. The instantaneous rate of change of a function for a given point.

This slope is a limit, and the derivative of the function at that point, if it exists, is exactly that limit.

We need to know this because it's FUNDAMENTAL for a concept you will absolutely need to know:

Differentiability