Really?
because A_{\mu} is not equal to A_{\nu} in general. So simply swapping the two indecies would just give,
A_{\nu}\partial_{\mu} - A_{\mu}\partial_{\nu}
leaving me with the same problem.
I was wondering why for
[tex]
F_{\mu \nu} = [D_{\mu},D_{\nu}] = \partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}+[A_{\mu},A_{\nu}]
[\tex]
the term
[tex]
A_{\mu}\partial_{\nu} - A_{\nu}\partial_{\mu}
[\tex]
vanishes.