Find the Gradient Field of the Function $$f ( x , y , z ) = \frac { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } { x ^ { 5 } }$$

question 84

Multiple Choice

Find the gradient field of the function.
- $$f ( x , y , z ) = \frac { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } { x ^ { 5 } }$$

• A) \({\nabla} f = \frac { 7 x ^ { 2 } + 5 y ^ { 2 } + 5 z ^ { 2 } } { x ^ { 6 } } \mathbf { i } + \frac { 2 y } { x ^ { 5 } } j + \frac { 2 z } { x ^ { 5 } } \mathbf { k }\)
• B)\({\nabla} f = \frac { 5 } { x ^ { 6 } } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) \mathbf { i } + \frac { 2 y } { x ^ { 5 } } j + \frac { 2 z } { x ^ { 5 } } \mathbf { k }\)
• C) \({\nabla} f = \frac { - 3 } { x ^ { 4 } } i + 2 y j + 2 z k\)
• D) \({\nabla} f = \frac { - 3 x ^ { 2 } - 5 y ^ { 2 } - 5 z ^ { 2 } } { x ^ { 6 } } i + \frac { 2 y } { x ^ { 5 } } j + \frac { 2 z } { x ^ { 5 } } k\)

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