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

• Comments, Questions?

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From the math blog...

Differentiation Java Applet (Polynomials)

You can use this Java applet to explore some of the differentiation examples in this chapter.

Things to Do

In this applet, there are pre-defined examples in the top pull-down menu. The examples are taken from this chapter.

In the left pane you will see the graph of the function of interest, and the graph of the first derivative is in the right pane.

1. Select one of the examples in the pull-down menu.
2. Use the slider at the bottom to change the x-value. You will see a red tangent line on the function graph move and you will see a red cross on the first derivative curve indicating the value of the first derivative for that x-value.
3. The third example, 2*x^3/(4-x), has an interesting graph. There is a discontinuity at x = 4. Either side of that discontinuity, the y-values go off to infinity, of course.
4. Change the minimum and maximum view limits for x and y to zoom in and out on portions of the graph.
5. Try your own graphs by typing them in at the bottom (next to "f(x)=") and pressing "New Function".

Note 1 - Multiplication: If you want to enter (say) 4 multiplied by x, you can't use "4x". You have to enter it using an asterix, like this: "4*x".

Note 2 - Functions: You must enter functions using brackets. For example, you cannot put "sin x". It must be "sin(x)".

Applet by David Eck and team from the Hobart and William Smith Colleges.

Sorry about the slow load time for this applet - it is pretty big...