(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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_{r}e_{r}+ F_{t}e_{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)

2. Relevant equations

x=rcost

y=rsint

Divergence formula in cartesian coordinates

3. The attempt at a solution

F(r,t) = (F_{r}cost - F_{t}sint, F_{r}sint + F_{t}cost, 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.

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# Divergence in plane polars

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