Find the Directional Derivative of the Given Function at the Specified

Multiple Choice

Find the directional derivative of the given function at the specified point $P$ in the direction $\vec { u }$ $f ( x , y ) = \cos ( x y ) , P = \left( 2 , \frac { \pi } { 6 } \right) , \vec { u } = \left\langle \frac { 3 } { \sqrt { 10 } } , \frac { 1 } { \sqrt { 10 } } \right\rangle$

A) $\frac { - 4 \sqrt { 10 } - \pi \sqrt { 30 } } { 40 }$
B) $- 3 \pi \sqrt { 3 } - 4 \sqrt { 3 }$
C) $\frac { \pi \sqrt { 3 } } { 12 } - \sqrt { 3 }$
D) $\frac { 3 \pi \sqrt { 3 } + 4 \sqrt { 3 } } { \sqrt { 10 } }$