Find the Directional Derivative of the Function at P in the Direction

Multiple Choice

Find the directional derivative of the function at P in the direction of $\overrightarrow { \mathbf { v } }$ $f ( x , y ) = 3 x - 2 x y + 7 y , P ( 1,9 ) , \quad \overrightarrow { \mathbf { v } } = \frac { 1 } { 2 } ( \hat { \mathbf { i } } + \sqrt { 3 } \hat { \mathbf { j } } )$

A) $\frac { - 15 + 5 \sqrt { 3 } } { 4 }$
B) $\frac { - 15 + 5 \sqrt { 3 } } { 2 }$
C) $\frac { 21 + 5 \sqrt { 3 } } { 2 }$
D) $\frac { 21 + 5 \sqrt { 3 } } { 4 }$
E) $\frac { - 15 + 9 \sqrt { 3 } } { 2 }$