∇ · (|r| r)
=|r| ∇ · ( r) + r ∇ · |r|
|r| =√x²+y²+z²
∇ · ( r) =dr/dx +dr/dy+dr/dz= i+j+k
so
∇ · (|r| r)
=√x²+y²+z² (i+j+k) + (x i + y j + z k ) ∇ · |r|
∇ · |r|= 2(x+y+z)/√x²+y²+z²
finally
∇ · (|r| r)
= |r| (i+j+k) + 2(xi+yj+zk)/ |r|=|r| (i+j+k) + 2r/|r|
