Answer
$\dfrac{\sqrt 3}{6}-\dfrac{1}{4}$
Work Step by Step
Formula to calculate the directional derivative: $D_uf=f_x(x,y)a+f_y(x,y)b$
$D_uf=\dfrac{1}{\sqrt {2x+3y}} \times \cos (-\pi/6)+\dfrac{3}{2\sqrt {2x+3y}} \times \sin (-\pi/6)$
This implies
At $(3,1)$
$D_uf(3,1)=\dfrac{1}{3} \times \dfrac{\sqrt 3}{2}+\dfrac{1}{2} \times \dfrac{-1}{2}$
$D_uf(3,1) =\dfrac{\sqrt 3}{6}-\dfrac{1}{4}$
