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) \({\nabla} f =\frac{1}{x^{2} y z} i+\frac{1}{x y^{2} z} j+\frac{1}{x y z^{2}} k\)

Grasp the basic principles of light and color vision including theories and biological mechanisms.

Know the structures and functions involved in the visual system.

Understand the physiological and psychological aspects of hearing.

Comprehend the mechanisms and theories related to color vision.

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