Use the Chain Rule to Find $\frac { \partial u } { \partial p }$

question 10

Multiple Choice

Use the Chain Rule to find $\frac { \partial u } { \partial p }$ .
$$u = \frac { x + y } { y + z }$$
$x = p + 3 r + 4 t , y = p - 3 r + 4 t , z = p + 3 r - 4 t$

• A) \(\frac { \partial u } { \partial p } = \frac { 12 t } { p ^ { 2 } } + t\)
• B) \(\frac { \partial u } { \partial p } = - \frac { 4 t } { p ^ { 2 } }\)
• C) \(\frac { \partial u } { \partial p } = - \frac { 12 t } { p ^ { 2 } }\)
• D) \(\frac { \partial u } { \partial p } = - \frac { 3 t } { p ^ { 3 } }\)
• E) \(\frac { \partial u } { \partial p } = \frac { 4 t } { p }\)

---

Definitions:

Exchange Rate

The value of one currency expressed in terms of another currency, used when converting from one currency to another.

Rupees

The official currency of India, also used as currency in other countries such as Pakistan, Nepal, and Sri Lanka.

United States Imports

Goods and services brought into the United States from other countries for sale or use.

Comparative Advantage

The ability of a country or individual to produce a particular good or service at a lower opportunity cost than its trade partners.