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

question 228

Multiple Choice

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

• A) \({\nabla} f = \frac { 1 } { \mathrm { x } ^ { 2 } } \mathrm { i } + \frac { 1 } { \mathrm { y } ^ { 2 } } \mathrm { j } + \frac { 1 } { \mathrm { z } ^ { 2 } } \mathbf { k }\)
• B) \({\nabla} f = - \frac { 1 } { \mathrm { x } ^ { 2 } } \mathrm { i } - \frac { 1 } { \mathrm { y } ^ { 2 } } \mathrm { j } - \frac { 1 } { \mathrm { z } ^ { 2 } } \mathrm { k }\)
• C) \({\nabla} f = - \frac { 1 } { x ^ { 2 } y z } \mathbf { i } - \frac { 1 } { x y _ { y } ^ { 2 } z } \mathbf { j } - \frac { 1 } { x y z ^ { 2 } } \mathbf { k }\)
• D) \({\nabla} f =\frac{1}{x^{2} y z} i+\frac{1}{x y^{2} z} j+\frac{1}{x y z^{2}} k\)

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