The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Chain Rule - Applications

The Chain Rule has two types of applications.

(1)    Given x = f(t) and y = G(x), find 02_differentiation-357.gif. Use 02_differentiation-358.gif

(2)    Given x = f(t) and y = g(t), find 02_differentiation-359.gif. Use 02_differentiation-360.gif02_differentiation-361.gif

Applications of type (1) often arise when a new dependent variable x is introduced to help compute 02_differentiation-362.gif. 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).

Last Update: 2006-11-05