Find the Gradient of the Function $f ( x , y , z ) = z ^ { 6 } e ^ { 2 x \sqrt { y } }$

question 9

Multiple Choice

Find the gradient of the function $f ( x , y , z ) = z ^ { 6 } e ^ { 2 x \sqrt { y } }$ .

• A) \(z e ^ { 2 x \sqrt { y } } \left\langle 2 z ^ { 5 } \sqrt { y } , \frac { x z ^ { 5 } } { \sqrt { y } } , 6 z ^ { 4 } \right\rangle\)
• B) \(e ^ { x ^ { 2 } \sqrt { y } } \left\langle 6 x z \sqrt { y } , \frac { x ^ { 2 } z } { 2 \sqrt { y } } , 2 \right\rangle\)
• C) \(z e ^ { x \sqrt { y } } \left\langle z \sqrt { y } , \frac { x z } { 2 \sqrt { y } } , 6 \right\rangle\)
• D) \(e ^ { x ^ { 2 } \sqrt { y } } \left\langle 2 x z \sqrt { y } , \frac { x ^ { 2 } z } { 6 \sqrt { y } } , 1 \right\rangle\)
• E) \(z e ^ { 2 x \sqrt { y } } \left\langle 2 z \sqrt { y } , \frac { x z } { \sqrt { y } } , 2 \right\rangle\)

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