\displaystyle $\begin{align} Df(x)(a) & = \frac{1}{1 + \| x \|^4} \cdot 2 (x | a) x + \arctan \| x \|^2 a \\ & = \left( \frac{n (n + 1)}{n^2 + 1} + \arctan n, \frac{n (n + 1)}{n^2 + 1} + 2 \arctan n, \ldots, \frac{n (n + 1)}{n^2 + 1} + n \arctan n \right)\end{align}$