Find the Directional Derivative of the Function $f ( x , y ) = ( x + 6 ) e ^ { y }$

question 118

Multiple Choice

Find the directional derivative of the function $f ( x , y ) = ( x + 6 ) e ^ { y }$ at the point $P ( 7,0 )$ in the direction of the unit vector that makes the angle $\theta = \frac { \pi } { 2 }$ with the positive $x$ -axis.
Select the correct answer.

• A) \(6 e ^ { 7 }\)
• B) 13
• C) 1
• D) \(e ^ { 7 }\)

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Definitions:

Mass Production

A manufacturing technique that involves the production of large quantities of standardized products, often using assembly lines or automated technology.

Mass Consumption

A socioeconomic phase characterized by the widespread purchase and use of goods and services by a large number of people in a society.

Mass Producer

A mass producer is a company or individual that manufactures goods in large quantities using standardized processes, usually to meet widespread consumer demand.

Productivity

A measure of the efficiency of production, often quantified as the ratio of output to inputs used in the production process.