I am learning classical field theory and am trying to find the momentum density of the electromagnetic lagrangian as part of an example of Noether's Theorem. The derivative I am encountering is: $$ \frac{\partial}{\partial(\partial_{\sigma}A_{\rho})} \left( \partial_{\mu}A_{\nu}\partial^{\mu}A^{\nu} \right). $$ I know that from here one uses chain rule to split it into two partial derivatives, and I know that in the end I should get a quantity that has upper indices $\sigma$ and $\rho$, since I am just taking the derivative of a scalar (indices are summed over).
I also realize that basically I am taking the derivative of "the square of the derivative of $A$", with respect to "the derivative of $A$", but I am confused as to how the indices work out.

I am learning classical field theory and am trying to find the momentum density of the electromagnetic lagrangian as part of an example of Noether's Theorem. The derivative I am encountering is: $$ \frac{\partial}{\partial(\partial_{\sigma}A_{\rho})} \left( \partial_{\mu}A_{\nu}\partial^{\mu}A^{\nu} \right). $$ I know that from here one uses chain rule to split it into two partial derivatives, and I know that in the end I should get a quantity that has upper indices $\sigma$ and $\rho$, since I am just taking the derivative of a scalar (indices are summed over).
I also realize that basically I am taking the derivative of "the square of the derivative of $A$", with respect to "the derivative of $A$", but I am confused as to how the indices work out.

edit: I should mention that all indices are 0,1,2,3.