Answer
$$\frac{\partial{u}}{\partial{x_{i}}}=\frac{2x_{i}}{2\sqrt{{(x_{1})}^2+...+{(x_{n})}^2}}=\frac{x_{i}}{\sqrt{{(x_{1})}^2+...+{(x_{n})}^2}}$$
Work Step by Step
$$u=\sqrt{{(x_{1})}^2+...+{(x_{n})}^2}$$
Select an arbitrary term $x_{i}$.
$$\therefore\frac{\partial{u}}{\partial{x_{i}}}=\frac{2x_{i}}{2\sqrt{{(x_{1})}^2+...+{(x_{n})}^2}}=\frac{x_{i}}{\sqrt{{(x_{1})}^2+...+{(x_{n})}^2}}$$
