Give an Appropriate Answer $$f ( x , y ) = \frac { e ^ { - x } } { x ^ { 2 } + y ^ { 2 } }$$

question 306

Multiple Choice

Give an appropriate answer.
- $$f ( x , y ) = \frac { e ^ { - x } } { x ^ { 2 } + y ^ { 2 } }$$

• A) \(\frac { \partial f } { \partial x } = - \frac { 2 x e ^ { - x } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } ; \frac { \partial f } { \partial y } = - \frac { 2 y e ^ { - x } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }\)
• B) \(\frac { \partial f } { \partial x } = \frac { e ^ { - x } \left( x ^ { 2 } + y ^ { 2 } + 2 x \right) } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } ; \frac { \partial f } { \partial y } = \frac { 2 y e ^ { - x } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }\)
• C) \(\frac { \partial f } { \partial x } = - \frac { e ^ { - x } \left( x ^ { 2 } + y ^ { 2 } + 2 x \right) } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } ; \frac { \partial f } { \partial y } = - \frac { 2 y e ^ { - x } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }\)
• D) \(\frac { \partial f } { \partial x } = - \frac { e ^ { - x } \left( x ^ { 2 } + y ^ { 2 } + x \right) } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } ; \frac { \partial f } { \partial y } = - \frac { y e ^ { - x } } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } }\)

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Definitions:

Standard Deviation

An indicator of the range of variability or spread within a series of numbers, showing the extent to which these numbers deviate from the average.

Mean Price

Mean price is the average price of a set of goods or services, calculated by dividing the total price by the number of items.

Item

An individual article or unit, especially one that is part of a list, collection, or set.

Stock Boys

Individuals responsible for stocking shelves, organizing products, and maintaining inventory in retail stores.