Find the Gradient Field of the Function ${\nabla} f = - z \cos ( x + y + z ) \mathbf { i } - z \cos ( x + y + z ) \mathbf { j } + ( \sin ( x + y + z ) - z \cos ( x + y + z ) ) \mathbf { k }$

question 151

Multiple Choice

Find the gradient field of the function.
-f(x, y, z) = z sin (x + y + z)

• A)\({\nabla} f = - z \cos ( x + y + z ) \mathbf { i } - z \cos ( x + y + z ) \mathbf { j } + ( \sin ( x + y + z ) - z \cos ( x + y + z ) ) \mathbf { k }\)
• B) \(\nabla \mathbf { f } = \cos x i \mathbf { i } + \cos y \mathbf { j } + ( \sin z + z \cos z ) \mathbf { k }\)
• C) \(\nabla \mathrm { f } = \mathrm { z } \cos ( \mathrm { x } + \mathrm { y } + \mathrm { z } ) \mathbf { i } + \mathrm { z } \cos ( \mathrm { x } + \mathrm { y } + \mathrm { z } ) \mathbf { j } + ( \sin ( \mathrm { x } + \mathrm { y } + \mathrm { z } ) + \mathrm { zcos } ( \mathrm { x } + \mathrm { y } + \mathrm { z } ) ) \mathbf { k }\)
• D)\({\nabla} f = - \cos x \mathbf { i } - \cos y \mathbf { j } + ( \sin z - z \cos z ) \mathbf { k }\)

---

Definitions:

Mental Retardation

An outdated and offensive term previously used to describe individuals with significantly below-average intellectual functioning and adaptive behaviors.

Special Education

Tailored educational programs designed to meet the unique needs of students with learning disabilities, physical disabilities, or other special needs.

Metabolic Disorder

A condition that occurs when the body's metabolic processes are disrupted, affecting the ability to convert food into energy.

Phenylketonuria

A genetic disorder characterized by the body's inability to break down the amino acid phenylalanine, leading to its accumulation and potential brain damage.