An Applet for Multivariable Visual Chain Rule

This applet looks at the chain rule in the case when a parameterized curve from R to R2 is composed with a function from R2 to R to produce a function from R to R.   The standard situation starts with a curve in the x-y plane parameterized by t, then considers z as a function of x and y. In the composition we then consider z a as a function of t.

In understanding this version of the chain rule we want to introduce a second parameter, s, so that we think of x as a function of s and y as a function of t.  The parameterized curve corresponds to the diagonal line in the s-t plane

You may find it useful to review the chain rule for functions of one variable.

The formula for the chain rule is Fromula
The applet has 4 windows, a control panel,  a Zxy window that plots z as a function of x and y, a Zst window that plots z as a function of s and t, and an "Edge and Diagonal Paths" window that shows curves together.

A Worksheet for the Chain Rule Applet for functions of two variables is available.

Things to notice:

This applet was designed as by modifying an applet from a demo by Tom Banchoff at Brown University.  It is used with permission.   Go to the Banchoff Applet Help page.

Return to the Banchoff Applet page.
Return to the SLU Calculus Applet page.

Return to the Saint Louis University Department of Mathematics and Computer Science home page

Last updated By Mike May, S.J. ,  October 6, 2006.