Find the Derivative of the Function at P0 in the Direction

question 10

Multiple Choice

Find the derivative of the function at P0 in the direction of u.
- $$f ( x , y ) = \tan ^ { - 1 } \frac { - 3 x } { y } , \quad P _ { 0 } ( - 7 , - 8 ) , \quad \mathbf { u } = 12 \mathbf { i } - 5 \mathbf { j }$$

• A) \(\frac { 393 } { 6565 }\)
• B) \(\frac { 456 } { 6565 }\)
• C) \(\frac { 27 } { 505 }\)
• D) \(\frac { 477 } { 6565 }\)

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Definitions:

Contribution Margin

The difference between sales revenue and variable costs of production, used to cover fixed costs and generate profit.

Controllable Fixed Costs

Fixed costs that management has the ability to influence or change in the short term, such as advertising expenses.

Controllable Margin

The portion of profit or contribution margin that a manager has direct control over, before fixed costs and overhead are deducted.

Responsibility Report

A management tool that collects and reports planned and actual financial information by responsibility centers.