Find the Derivative of the Function at P0 in the Direction

question 198

Multiple Choice

Find the derivative of the function at P0 in the direction of u.
- $$f ( x , y , z ) = \tan ^ { - 1 } \frac { 4 x } { 2 y + 4 z } , \quad P _ { 0 } ( - 9,0,0 ) , \quad \mathbf { u } = 12 \mathbf { i } - 3 \mathbf { j } + 4 \mathbf { k }$$

• A) \(\frac { 2 } { 117 }\)
• B) \(\frac { 1 } { 78 }\)
• C) \(\frac { 1 } { 117 }\)
• D) \(\frac { 5 } { 234 }\)

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Definitions:

Cognitive Therapy

A form of psychotherapy that aims to change negative patterns of thinking to improve an individual's mood and behaviors.

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The cognitive process of looking for reasons, forming conclusions, judgments, or inferences from facts or premises.

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A cognitive-behavioral therapy technique that involves reducing the irrational fear associated with exaggerated or worst-case scenario thinking.

Psychotherapy

A treatment method for mental health issues that involves talking with a therapist to explore and overcome personal challenges.