I am currently trying to show the following equation which, appears from the Euler Lagrange equation:
$$\frac{\partial}{\partial \partial_{\nu} A^{\mu} } \left( \frac{1}{4} F_{\mu \nu} F^{\mu \nu} \right) = F_{\nu\mu}$$ with $$F^{\mu \nu} = \partial_{\mu}A^{\nu} - \partial_{\nu}A^{\mu}$$
However, I'm having a hard time working with the co-/ contravariant Tensors that appear. I am working on some similar equations too, so I would be glad, if someone could help me with this one, so I can solve the rest myself.