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:

Line-Angle Structure

A simplified way to draw organic molecules where lines represent bonds and the ends of lines or intersections represent carbon atoms.

Line-Angle Formula

A simplified chemical drawing that uses lines to represent bonds between atoms, omitting the symbols for carbon and hydrogen atoms.

Skeletal Structure

A simplified representation of organic molecules highlighting the bonds between carbon atoms without explicitly drawing hydrogen atoms.

Condensed Formulas

A method of writing a formula of a compound using the line bond structure but omitting the lines representing bonds to simplify the representation.