The purpose of this applet is to illustrate the chain rule:

if y(x) = g[f(x)] then y'(x) = g'[f(x)]*f'(x)

The applet shows the graphs of two functions, f(x) and g(x), and of their composition, g[f(x)]. The user can drag the red square back and forth on the x-axis of the graph of f(x). This square determines an x-value, X. The points (X, f(X)), (f(X), g[f(X)]), and (X, g[f(X)]) are marked on the respective graphs. Tangent lines are drawn at these points, as well as the slope of each line, at each of these points, in order to illustrate the chain rule. In terms of the calculated slopes, the slope of the tangent line of the composite function in the third window on the right should equal the product of the two slopes (derivatives) displayed in the first two windows on the left.

The applet will respond to mouse actions on the canvas. Note that each coordinate rect can be resized independently using these actions, but the buttons at the lower right affect all the coordinate rects. The applet is also configured with several loadable examples. The user may enter functions of this form in the "f(x)=" and "g(x)=" input box or use the mouse to define new functions.