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The Derivative

The Derivative

Author: c o
Description:

To define the derivative of a function at a point
To look at the graphs of functions along side the graphs of their derivatives
To show an example of how a derivative function is found in general

This packet introduces the derivative of a function, which is a central pillar of calculus.

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Tutorial

Prerequisite Material

Before starting this packet you ought to be comfortable working with limits and with finding the slope of a line tangent to a curve.

Introducing Derivatives

This video builds on the learner's experience with finding the slope of a line tangent to a graph to define the derivative of a function.

Visualizing Derivatives

In this video we look at several examples of functions plotted on the same set of axes as their derivatives in order to better see their relationship.

Derivative Of X To The Nth Power

In this video we see an example of finding the general form of the derivative of f(x) = x^n for some exponent n.