Answer
$\dfrac{7}{2}(\sqrt3+1)$
Work Step by Step
Formula to calculate the directional derivative: $D_uf=f_x(x,y)a+f_y(x,y)b$
$D_uf=(3x^2y^4+4x^3y^3) \times \cos (\pi/6)+(4x^3y^3+3x^4y^2) \times \sin (\pi/6)$
This implies
At $(1,1)$
$D_uf(1,1)=7 \times \dfrac{\sqrt 3}{2}+7 \times \dfrac{1}{2}$
$D_uf(1,1) =\dfrac{7}{2}(\sqrt3+1)$
