Solution
= Solution
The <gradient> is $\nabla f=(2x,z,y)$, so its value at the point is $(2,-3,1)$. Since the specified direction is already a <unit vector>, the <directional derivative> is its <dot product> with that <gradient>:
$$
\boxed{D_{\hat{\mathbf u}}f=\frac{(2,-3,1)\cdot(2,1,2)}3
=\frac{4-3+2}{3}=1}.
$$