2. If u = xy
z for x, y, and z > 0, then
|
A. 3u |
B. u(1 + z + z2/y) |
C. u(1 +y ln z +z ln y) |
|
D. u(1 + z2/y + y ln z) |
E. u(1 + z + z ln y) |
Solution: The answer is E
Take the partial derivative of u with respect to x, y, and z, as follows:
Substitute these values into the above equation:
Note: When taking the partial derivative of u with respect to z, rewrite yz as ez ln y and then differentiate.