Answer
$-2.83$
Work Step by Step
Our aim is to determine the directional derivative. In order to find it we have to use the expression:
$D_uf(x,y)=f_x(x,y)m+f_y(x,y)n$
or, $D_uf(x,y)=\nabla f(x,y) \cdot u=\nabla f(x,y) \cdot \dfrac{v}{|v|}$
From the given figure, we see that $\theta=180^\circ+45^\circ=225^\circ$ or, $\dfrac{5\pi}{4}$
Also, $(x,y)=(2,2)$ [given]
$D_uf (2,2)=(4)(1) (\dfrac{5\pi}{4})=-2.83$
