Find the Gradient Vector Field of the Function $f ( x , y ) = \arctan \left( \frac { y } { x } \right)$

question 207

Multiple Choice

Find the gradient vector field of the function $f ( x , y ) = \arctan \left( \frac { y } { x } \right)$ .

• A) \(\left( \frac { y } { x ^ { 2 } + y ^ { 2 } } , \frac { x } { x ^ { 2 } + y ^ { 2 } } \right)\)
• B)\(\left( \frac { - y } { x ^ { 2 } + y ^ { 2 } } , \frac { - x } { x ^ { 2 } + y ^ { 2 } } \right)\)
• C)\(\left( \frac { y } { x ^ { 2 } + y ^ { 2 } } , \frac { - x } { x ^ { 2 } + y ^ { 2 } } \right)\)
• D)\(\left( \frac { - y } { x ^ { 2 } + y ^ { 2 } } , \frac { x } { x ^ { 2 } + y ^ { 2 } } \right)\)
• E)\(\left( \frac { x } { x ^ { 2 } + y ^ { 2 } } , \frac { y } { x ^ { 2 } + y ^ { 2 } } \right)\)
• F)\(\left( \frac { - x } { x ^ { 2 } + y ^ { 2 } } , \frac { - y } { x ^ { 2 } + y ^ { 2 } } \right)\)
• G)\(\left( \frac { x } { x ^ { 2 } + y ^ { 2 } } , \frac { - y } { x ^ { 2 } + y ^ { 2 } } \right)\)
• H)\(\left( \frac { - x } { x ^ { 2 } + y ^ { 2 } } , \frac { y } { x ^ { 2 } + y ^ { 2 } } \right)\)

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Definitions:

Variable Overhead Efficiency Variance

The difference between the actual hours taken to produce something and the standard hours expected, multiplied by the variable overhead rate per hour.

Manufacturing Overhead

All indirect costs associated with manufacturing a product, excluding direct materials and direct labor costs.

Variable Overhead Rate Variance

The difference between the actual variable overhead incurred and the expected (or standard) cost based on the actual level of activity.

Variable Manufacturing Overhead

Overhead costs that fluctuate with the level of production, such as utilities or raw materials.