Chapter Contents

Differentiation
1. Limits and Differentiation
2. The Slope of a Tangent to a Curve (Numerical)
3. The Derivative from First Principles
4. Derivative as an Instantaneous Rate of Change
5. Derivatives of Polynomials
6. Derivatives of Products and Quotients
Differentiation Java applet
Derivative of a Cubic - Exploration using GeoGebra
7. Differentiating Powers of a Function
8. Differentiation of Implicit Functions
9. Higher Derivatives
10. Partial Derivatives
Differentiation Problem Solver

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Derivative of a Cubic - Exploration using GeoGebra

by M. Bourne

You are looking at the graph of a cubic polynomial, f(x) = x³ − 4x² + x + 6 (in blue).

The green curve is the first derivative of f(x).

Directions: Click on the point A and drag it slowly left or right. You will see the slope of the curve change as well as a trace of the point B, which is on the first derivative curve.

For an explanation of how this interactive was created using GeoGebra, see
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Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Differentiation Java applet

7. Differentiating Powers of a Function

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