Let $f ( x , y ) = x e ^ { y } + y e ^ { x }$ Then the directional derivative of f at (0,0) in the direction of the unit vector $\mathbf { U }$ which makes an angle of $\frac { \pi } { 6 }$ from the positive x-axis is

A) $\frac { \sqrt { 3 } + 1 } { 2 }$
B) $\frac { \sqrt { 3 } - 1 } { 2 }$
C) $- \frac { \sqrt { 3 } - 1 } { 2 }$
D) $- \frac { \sqrt { 3 } - 1 } { 2 }$.
E) $\frac { \sqrt { 3 } + 3 } { 2 }$

Question

Let

f ( x , y ) = x e ^ { y } + y e ^ { x }

Then the directional derivative of f at (0,0) in the direction of the unit vector

\mathbf { U }

which makes an angle of

\frac { \pi } { 6 }

from the positive x-axis is

A) $\frac { \sqrt { 3 } + 1 } { 2 }$
B) $\frac { \sqrt { 3 } - 1 } { 2 }$
C) $- \frac { \sqrt { 3 } - 1 } { 2 }$
D) $- \frac { \sqrt { 3 } - 1 } { 2 }$.
E) $\frac { \sqrt { 3 } + 3 } { 2 }$

Quizplus · Accepted Answer

The Answer is A

Let f(x,y)=xey+yexf ( x , y ) = x e ^ { y } + y e ^ { x }f(x,y)=xey+yex

Let $f ( x , y ) = x e ^ { y } + y e ^ { x }$