If $f ( x , y ) = \ln \left( x y ^ { 4 } + 7 \right),$

question 22

Multiple Choice

If $f ( x , y ) = \ln \left( x y ^ { 4 } + 7 \right) ,$ find $\frac { \partial f } { \partial x } \text { and } \frac { \partial f } { \partial y }$

• A) \(\frac { \partial f } { \partial x } = \frac { x } { x y ^ { 4 } + 7 } , \frac { \partial f } { \partial y } = \frac { y ^ { 4 } } { x y ^ { 4 } + 7 }\)
• B) \(\frac { \partial f } { \partial x } = \frac { y ^ { 4 } } { x y ^ { 4 } + 7 } , \frac { \partial f } { \partial y } = \frac { 4 x y ^ { 3 } } { x y ^ { 4 } + 7 }\)
• C) \(\frac { \partial f } { \partial x } = \frac { 1 } { y ^ { 4 } } , \quad \frac { \partial f } { \partial y } = \frac { 1 } { 4 x y ^ { 3 } }\)
• D) \(\frac { \partial f } { \partial x } = \frac { x y ^ { 4 } + 7 } { y ^ { 4 } } , \quad \frac { \partial f } { \partial y } = \frac { 4 x y ^ { 4 } + 7 } { x y ^ { 3 } }\)
• E) \(\frac { \partial f } { \partial x } = \ln \left( \frac { 1 } { y ^ { 4 } } \right) , \quad \frac { \partial f } { \partial y } = \ln \left( \frac { 1 } { 4 x y ^ { 3 } } \right)\)

---

Definitions:

Treasury Bills

Short-term government securities issued at a discount from the face value and maturing at their face value to create a return to the investors.

Collection Time

The average period it takes for a business to receive payments owed by its customers after a sale has been made.

Lockbox System

A service provided by banks to companies for receiving payments from customers; payments are sent to a post office box and then quickly processed by the bank.

Money Market Securities

Money Market Securities are short-term debt instruments that are highly liquid and considered safe, such as Treasury bills, certificates of deposit, and commercial paper.