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)\({\nabla} f = - \cos x \mathbf { i } - \cos y \mathbf { j } + ( \sin z - z \cos z ) \mathbf { k }\)

Recognize the steps for establishing a two-chamber waterless chest tube system.

Identify and respond to emergency conditions related to chest tube patients, such as tension pneumothorax.

Describe the nurse's roles and responsibilities during chest tube removal.

Evaluate expected outcomes and normal drainage amounts post chest tube insertion.

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