Find the Gradient of the Function $f ( x , y , z ) = z ^ { \gamma } e ^ { 2 x \sqrt { y } }$

question 2

Multiple Choice

Find the gradient of the function $f ( x , y , z ) = z ^ { \gamma } e ^ { 2 x \sqrt { y } }$ .

• A)
• \(e ^ { x ^ { 2 } \sqrt { y } } \left( 7 x z \sqrt { y } , \frac { x ^ { 2 } z } { 2 \sqrt { y } } , 2 \right)\)
• B)
• \(z e ^ { x \sqrt { y } } \left( z \sqrt { y } , \frac { x z } { 2 \sqrt { y } } , 7 \right)\)
• C)
• \(e ^ { x ^ { 2 } } \sqrt { y } \left( 2 x z \sqrt { y } , \frac { x ^ { 2 } z } { 7 \sqrt { y } } , 1 \right)\)
• D)
• \(z e ^ { 2 x \sqrt { y } } \left( 2 z \sqrt { y } , \frac { x z } { \sqrt { y } } , 2 \right)\)
• E)
• \(z e ^ { 2 x \sqrt { y } } \left( 2 z ^ { 6 } \sqrt { y } , \frac { x z ^ { 6 } } { \sqrt { y } } , 7 z ^ { 5 } \right)\)

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Definitions:

Performance Productivity

Measures the efficiency of production in terms of output per unit of input, often used to assess workforce effectiveness.

Team Cohesion

it involves the extent to which team members stick together and remain united in pursuing their goals and objectives.

Clearly Defined Goals

Specific, explicit, and unambiguous objectives set forth for individuals or teams to aim for, facilitating focused efforts and clearer benchmarks for performance.

Great Teamwork

The effective and harmonious collaboration and cooperation among team members to achieve common goals.