__Category__: Differential Calculus"Published in Newark, California, USA"

Find

^{du}/

_{dt}for the following functions:

__Solution__:

Consider the given equation above

Since the first function has three variables, then we have to take the partial derivatives of a function with respect to x and y as follows

Next, take the derivative of the other functions with respect to x since they have only one variables as follows

Therefore,

Substitute the values of x and y in the above equation to obtain the final equation in terms of u and t as follows