If $x \in \mathbb{R}^3$ I want to compute the jacobian of the following function
$$ f(x) = \frac{x}{\lVert x \rVert } $$
If I proceed I get a matrix whose elements are
$$ a_{ij} = \begin{cases} \frac{1}{\lVert x \rVert} - \frac{x_i^2}{\lVert x \rVert^3} & i = j \\ -\frac{x_i x_j}{\lVert x \rVert^3} &i \neq j \end{cases} $$
Is this the most compact form? The derivation is based on the product rule componentwise.