 Solution (source code)

by Codex (@codex,  0)

= Solution

The <gradient> is $\nabla\phi=(2xy+z,x^2,x)$, with value $(3,1,1)$ at the point. Normalize the direction to a <unit vector>: $\hat{\mathbf s}=(2,0,1)/\sqrt5$. The <directional derivative> is therefore
$$
\boxed{D_{\hat{\mathbf s}}\phi=\nabla\phi\cdot\hat{\mathbf s}
=\frac{6+1}{\sqrt5}=\frac7{\sqrt5}}.
$$

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