Find the Gradient Field of the Function $$f ( x , y , z ) = x ^ { 6 } y ^ { 9 } + \frac { x ^ { 6 } } { z ^ { 8 } }$$

question 213

Multiple Choice

Find the gradient field of the function.
- $$f ( x , y , z ) = x ^ { 6 } y ^ { 9 } + \frac { x ^ { 6 } } { z ^ { 8 } }$$

• A) \({\nabla} f = \left( 6 \mathrm { x } ^ { 5 } + 6 \mathrm { x } ^ { 5 } \right) \mathbf { i } + 9 \mathrm { y } ^ { 8 } \mathbf { j } + \frac { 8 } { \mathrm { z } ^ { 9 } } \mathbf { k }\)
• B) \({\nabla} f = \left( 6 \mathrm { x } ^ { 5 } + 6 \mathrm { x } ^ { 5 } \right) \mathbf { i } + 9 \mathrm { y } ^ { 8 } \mathrm { j } - \frac { 8 } { \mathrm { z } ^ { 9 } } \mathbf { k }\)
• C) \({\nabla} f = \left( 6 x ^ { 5 } y ^ { 9 } + \frac { 6 x ^ { 5 } } { z ^ { 8 } } \right) i + 9 x ^ { 6 } y ^ { 8 } j - \frac { 8 x ^ { 6 } } { z ^ { 9 } } k\)
• D)\({\nabla} f = 6 x ^ { 5 } y ^ { 9 } i + 9 x ^ { 6 } y 8 - \frac { 8 x ^ { 6 } } { z ^ { 9 } } k\)

---

Definitions:

Behavioral Measures

Personality assessments that involve observing an individual’s behavior in a controlled situation.

Personality

The combination of characteristics or qualities that form an individual's distinctive character.

Rorschach Ink Blot Test

A psychological test in which individuals' perceptions of inkblots are used to analyze their personality and emotional functioning.

Abstract Stimuli

Non-concrete factors or elements that can influence behavior, perception, or performance, often in psychological contexts.