Find the Directional Derivative of the Function $f ( x , y ) = ( x + 5 ) e ^ { y }$

question 41

Multiple Choice

Find the directional derivative of the function $f ( x , y ) = ( x + 5 ) e ^ { y }$ at the point $P ( 6,0 )$ in the direction of the unit vector that makes the angle $\theta = \frac { \pi } { 2 }$ with the positive x-axis.

• A) \(e ^ { 6 }\)
• B) 1
• C) \(5 e ^ { 6 }\)
• D) 11

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Definitions:

Entire Body

Referring to the whole of a person's or organism's body including all of its parts and systems.

Parietal Lobe

A region of the brain located at the upper back area in the skull, crucial for processing sensory information from various parts of the body, understanding spatial orientation, and navigation.

Frontal Lobe

The part of the brain located at the front of the cerebral cortex, responsible for executive functions such as decision-making, problem-solving, and controlling behavior and emotions.

Occipital Lobe

The region of the cerebral cortex located at the back of the brain, responsible for processing visual information.