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

question 58

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.

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

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Definitions:

Teres Major

A muscle of the upper limb that assists in the rotation and adduction of the arm.

Teres Minor

A small muscle of the rotator cuff that assists in rotating the arm laterally and stabilizing the shoulder joint.

Lateral Rotation

The outward rotation of a limb or organ away from the midline of the body.

Medial Rotation

Medial rotation is a rotational movement toward the midline of the body, typically referring to a movement of the limbs.