1. If u = ex/y, x = 2r - s, and y = r + 2s for r + 2s non-zero, then, in terms of x and y, the partial derivative of u with respect to r is,

 

A. ((2-x)/y)ex/y

B. 3ex/y

C. (2/y)ex/y

D. ((2y-x)/y2)ex/y

E. ((2y-x)/y)ex/y

 

Solution: The answer is D

 

Given u as a function of x and y, where u is defined as,

we can take the partial derivative, with respect to r, of both sides of the above equation by using the chain rule and quotient rule for derivatives as follows,

Since,

and

 

then,

and

So, the partial derivative of u with respect to r, is given by,