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:

Random Numbers

Numerical values generated in such a way that each possible number has an equal chance of being selected, often used in simulations and cryptographic applications.

Time Compression

Techniques or strategies aimed at reducing the time needed to complete processes or activities, thereby increasing efficiency.

Trial and Error

A problem-solving method involving repeated, varied attempts which are continued until success, or until the practicer stops trying.

Monte Carlo Analysis

A computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making.