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) \(\frac { \partial f } { \partial x } = \ln \left( \frac { 1 } { y ^ { 4 } } \right) , \quad \frac { \partial f } { \partial y } = \ln \left( \frac { 1 } { 4 x y ^ { 3 } } \right)\)

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Definitions:

Dynamic Pricing

Refers to the process of charging different prices for goods or services based on the type of customer, time of the day, week, or even season, and level of demand.

Selling Season

The specific time period during which demand for a particular product or service is significantly higher, often due to seasonal factors.

Monopolistic Competition

A market structure characterized by many firms selling products that are similar but not identical, allowing for significant differentiation.

Differentiate

To distinguish a product, service, or brand from competitors by emphasizing unique features or benefits.