Answer
$\dfrac{\sqrt 2}{2}$
Work Step by Step
Formula to calculate the directional derivative: $D_uf=f_x(x,y)a+f_y(x,y)b$
$D_uf=(-y^2 \sin xy) \times \cos (\pi/4)+(\cos xy -xy \sin xy) \times \sin (\pi/4)$
This implies
At $(0,1)$
$D_uf(0,1)=0 \times \dfrac{\sqrt 2}{2}+1 \times \dfrac{\sqrt 2}{2}$
$D_uf(0,1) =\dfrac{\sqrt 2}{2}$
