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) \(z e ^ { 2 x \sqrt { y } } \left\langle 2 z \sqrt { y } , \frac { x z } { \sqrt { y } } , 2 \right\rangle\)

Comprehend the qualification and deduction amounts for education-related expenses under different tax credits.

Identify eligibility for the credit for the elderly or the disabled based on age, AGI, and filing status.

Calculate the premium tax credit for health insurance purchased through the Marketplace.

Understand the conditions and limits of the earned income credit (EIC) for taxpayers with and without children.

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