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:

Myelin

A fatty substance that surrounds and insulates the axons of many neurons, improving the speed at which electrical impulses propagate along the nerve cells.

Skin Cells

The cells that constitute the outermost layer of the human body, playing crucial roles in protection, sensation, and regulation.

Neurons

Specialized cells in the nervous system that transmit information to other nerve cells, muscle, or gland cells.

Glia

Non-neuronal cells in the central and peripheral nervous systems that do not produce electrical impulses but are critical for the support, protection, and nutrition of neurons.