Answer
$-2.83$
Work Step by Step
Formula to calculate the directional derivative: $D_uf=\nabla f(x,y) \cdot
u$
From the given figure, we have $\theta=180^\circ+45^\circ=225^\circ$ or, $\dfrac{5\pi}{4}$
At $(2,2)$
$D_uf (2,2)=(4)(1) \cdot \dfrac{5\pi}{4}$
Hence, $D_uf (2,2)=-2.83$
