Discussion:  Roundtable 
Topic:  "Graphing Calculator" Software 
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Subject:  The Chain Rule 
Author:  Gene 
Date:  Sep 24 2003 
focusing on using the definition of the derivative to develop the formulas. I
couldn't find any appropriate tools for what I wished to do here, although there
are some good practice differentiation applets I'll use after trig functions. It
would be nice to have something to help folks remember the quotient rule which
seems fraught with possibilities for errors. Anyone have suggestions?
I showed this function composition applet in class:
http://math.hws.edu/javamath/config_applets/FunctionComposition.html/.
If the red dot on the first graph is on the point (X, f(X)) say, the middle
graph obligingly shows the point (f(X), g(f(X))), while the final panel shows
(X, g(f(x))). If you wish you can put in your own functions g and f.
A little below the above applet you come to "Launch Function Composition." Do so
and you get the above figure with tangent lines. Miraculously (for those
skeptical of the Chain Rule) the product of the slopes of the functions in the
first two graphs is the slope of the function in the third graph.
There’s a pulldown menu at the top with some examples worth mulling about
(the first couple have absolute values which are quite illustrative in this
case). Note that you have to click Launch Applet after making the pulldown
menu choice. And you can always put in functions you're curious about.
 
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