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:

Brachial Vein

A vein located in the upper arm that accompanies the brachial artery and is involved in returning deoxygenated blood back to the heart.

Axillary Vein

A large blood vessel that conveys blood from the lateral aspect of the thorax, axilla, and upper limb toward the heart.

Veins

Blood vessels that carry deoxygenated blood towards the heart from the body's tissues.

Tunica Media

The middle layer of the wall of blood vessels, made up of smooth muscle cells and elastic fibers.