show that the divergence of the unit vecotor r is 2/r

I have done this using cartesian coordinates which is quite tedious,i was hoping someone could show me a way to do it with tensors

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- May 29th 2011, 05:06 PMulysses123divergence of unit vector
show that the divergence of the unit vecotor r is 2/r

I have done this using cartesian coordinates which is quite tedious,i was hoping someone could show me a way to do it with tensors - May 29th 2011, 07:30 PMTheEmptySet
First we need to know that

is a basis and

we have the 1-form

The divergence is given by

where * is the Hodge Dual

This gives a two form, now taking the derivative

This gives a three form and now taking the dual gives a 0-form

So this is the divergence in spherical coordinates.