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