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

Multiple Choice

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) $\frac { \sqrt { 3 } + 3 } { 2 }$