设函数 $u(x, y, z) = 1 + \frac{x^2}{6} + \frac{y^2}{12} + \frac{z^2}{18}$ , 单位向量 $\boldsymbol{n} = \frac{1}{\sqrt{3}} (1, 1, 1)$ , 则 $\left.\frac{\partial u}{\partial \boldsymbol{n}}\right|_{(1, 2, 3)} =$ ______.