Proving the Divergence Formula for Plane Polars

[Kate2010]

Homework Statement

I have to prove the divergence formula for plane polars. The question goes something like:

Find the divergence of the vector field F(r,t) = F_re_r + F_te_t where r and t are polar coordinates and e_r = (cos t, sin t, 0) and e_t = (- sin t, cos t, 0)
(t is theta in the question but t was easier to type)

Homework Equations

x=rcost
y=rsint
Divergence formula in cartesian coordinates

The Attempt at a Solution

F(r,t) = (F_rcost - F_tsint, F_rsint + F_tcost, 0)

Could I partially differentiate the first bit with respect to r and the second bit with respect to t, just ignoring the 0 at the end? This does not seem right, I'm not sure if it is even possible.

Or I feel like the chain rule might come into it somewhere?

I really don't know where to start.

 

[Kate2010]

Solved it :)