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Friday, February 7, 2014

Derivative - Chain Rule, 4

Category: Differential Calculus, Algebra

"Published in Vacaville, California, USA"

Given the following functions:



Find dy/dx.

Solution:

The first thing that we need to do is to get the derivative of the given functions with respect to their independent variables. 

Take the derivative of the first equation with respect to u, we have
 










Take the derivative of the second equation with respect to x, we have 




Since there are three variables in the given functions, then we have to use the Chain Rule in getting dy/dx, we have


Substitute the values of dy/du and du/dx to the above equation, we have



but


then the above equation becomes