Chain Rule - Applications

The Chain Rule has two types of applications.

(1)    Given x = f(t) and y = G(x), find . Use

(2)    Given x = f(t) and y = g(t), find . Use

Applications of type (1) often arise when a new dependent variable x is introduced to help compute . Applications of type (2) arise when two variables x and y both depend on a third variable t, for example, when x and y are the coordinates of a moving particle and t is time.

We give three examples of type (1) and then two of type (2).