Answer
$$\dfrac{\sqrt 2}{2}$$
Work Step by Step
Our aim is to determine the directional derivative. In order to find it we have to use the expression:
$D_uf(x,y)=f_x(x,y)m+f_y(x,y)n$
Given: $f(x,y)=y \cos (xy)$
$D_uf(x,y)=(-y^2 \sin xy) \times \cos (\pi/4)+(\cos xy -xy \sin xy) \times \sin (\pi/4)$
From the given data, we have: At $(0,1)$
$D_uf(0,1)=0 \times (\dfrac{\sqrt 2}{2})+1 \times (\dfrac{\sqrt 2}{2}) =\dfrac{\sqrt 2}{2}$
