Решение.\[ \begin{align}
& \varphi =x\cdot y+{{z}^{2}},\ grad\varphi =\frac{d\varphi }{dx}i+\frac{d\varphi }{dy}j+\frac{d\varphi }{dz}k. \\
& \frac{d\varphi }{dx}=(x\cdot y+{{z}^{2}})\prime =y,\ \frac{d\varphi }{dy}=(x\cdot y+{{z}^{2}})\prime =x,\ \frac{d\varphi }{dz}=(x\cdot y+{{z}^{2}})\prime =2\cdot z. \\
& grad\varphi =yi+xj+2\cdot zk \\
& grad\varphi =2i+2,7j+4k. \\
& \left| grad\varphi \right|=\sqrt{{{(\frac{d\varphi }{dx})}^{2}}+{{(\frac{d\varphi }{dy})}^{2}}+{{(\frac{d\varphi }{dz})}^{2}}},\ \left| grad\varphi \right|=\sqrt{{{(2)}^{2}}+{{(2,7)}^{2}}+{{(4)}^{2}}}=5,2. \\
\end{align} \]