Chain Rule with Pair of Levers
This applet illustrates the chain rule, which we use to find the derivative of a composite function, which depends on both of the component functions. A pair of levers is a good physical example of a composition function, where the output of the "inner function" becomes the input of the "outer function." This means that the composite function changes depending on how the inner and the outer functions change. In the applet, you can think of the blue line as the first, or inner, function and the red line as the second, outer function. The black segment joining them shows the change from output to input. You can change the input (dx) by sliding the black point up or down. Observe how this changes its output du (which is the input to the red line) and thus changes the final output (dy). *Important Note: In this case, the rates of change are constant because we are dealing with linear functions (whose derivatives are constant) . As we have seen in other cases, derivatives can depend on your input, which you should take into account when applying the Chain Rule.