Find the divergence of (xi + yj + zk)(x² + y² + z²)^-3/2. (this is r^-3)

We get

(div(xi + yj + zk))(x² + y² + z²)^-3/2 + (xi + yj + zk)(x² + y² + z²)^-3/2

or

3(x² + y² + z²)^-3/2 - (3/2) (xi + yj + zk)(2xi + 2yj + 2zk) (x² + y² + z²)^-5/2

which is 0, where the derivatives exist, which is everywhere but at the origin.