Find the Gradient of the Function $f ( x , y , z ) = z ^ { 7 } e ^ { 2 x \sqrt { y } }$

question 95

Multiple Choice

Find the gradient of the function $f ( x , y , z ) = z ^ { 7 } e ^ { 2 x \sqrt { y } }$ .

• 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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