Find the Gradient Vector Field Of $f$ Select the Correct Answer

question 124

Multiple Choice

Find the gradient vector field of $f$ . Select the correct answer.
$$f ( x , y , z ) = \sqrt { x ^ { 2 } + 4 y ^ { 2 } + 6 z ^ { 2 } }$$

• A) \(\frac { y } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { i } + \frac { x } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { j } + \frac { z } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { k }\)
• B) \(\frac { 1 } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { i } + \frac { 1 } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { j } + \frac { z } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { k }\)
• C)
• \(\frac { 2 x } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { i } + \frac { 2 y } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { j } + \frac { 2 z } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { k }\)
• D)
• \(\frac { x } { \sqrt { x ^ { 2 } + 4 y ^ { 2 } + 6 z ^ { 2 } } } \mathbf { i } + \frac { 4 y } { \sqrt { x ^ { 2 } + 4 y ^ { 2 } + 6 z ^ { 2 } } } \mathbf { j } + \frac { 6 z } { \sqrt { x ^ { 2 } + 4 y ^ { 2 } + 6 z ^ { 2 } } } \mathbf { k }\)
• E) None of these

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