Chain rule for derivatives

For functions

and

, differentiable at a point, the chain rule says that

In the applet below the display panel has these parts. For a particular choice of

, he first panel displays tangent to the graph of

; the second panel displays the tandent to the graph of

at the point

and the third panel displays the tangent to the graph of

. The slope of each tangent is given by the hight of the hight
angled triangle at the point. You can move the point

(the red box in first panel) or enter a specific value in the box for

. Select any one of he sample functions from the drop-
down menu and slick the button sample