This site provides users with interactive applet for exploring the intuitive notion of the chain rule.
In the applet we see an x-wheel, a u-wheel, and a y-wheel. You can change the speed of the x-wheel, and you can connect the wheels with belts and change their radii. You can use this model to explore the chain rule and try to get an intuitive understanding of where the formula comes from.
It asks the user several interactive questions and it also allows the user to cross the belt to explore the inverse relationship on the overall product.
It explains the chain rule with examples.