Find the Derivative of the Function at P0 in the Direction

question 150

Multiple Choice

Find the derivative of the function at P0 in the direction of u.
- $$f ( x , y ) = \ln ( x + 9 y ) , \quad P _ { 0 } ( 9 , - 9 ) , \quad u = 6 i + 8 j$$

• A) \(- \frac { 68 } { 45 }\)
• B) \(- \frac { 44 } { 45 }\)
• C) \(- \frac { 4 } { 3 }\)
• D) \(- \frac { 52 } { 45 }\)

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Definitions:

Differential Analysis

The process of comparing the costs and benefits of alternative decisions or investments to determine the best option.

Book Value

The value of an asset according to its balance sheet account balance, taking into account the cost of the asset minus any depreciation, amortization, or impairment costs.

Annual Costs

The total amount of expenditures associated with the ongoing operations of a business or project over the course of a year.

Opportunity Cost

The cost of forgoing the next best alternative when making a decision; represents the benefits that could have been received by choosing the alternative.