Tensor Derivatives (Derivation of the electromagnetic energy stress tensor)

I have the task to derive the electromagnetic energy stress tensor. I'm pretty new to the tensor index notation and I have a problem with an occuring derivative.

I have to verify that $\frac{\partial \mathcal{L}}{\partial (\partial_{\mu} A_{\lambda})}=-F^{\mu \lambda}$ with $\mathcal{L}=-\frac{1}{2}(\partial^{\mu}A^{\nu}\partial_{\mu}A_{\nu}-\partial^{\mu}A^{\nu}\partial_{\nu}A_{\mu})$

Can someone please show me step by step how to do this derivative? I understand the tensor notation itself but I have problems to understand such a derivative, especially when I have a term like $\frac{\partial(\partial^{\mu}A^{\nu})}{\partial(\partial_{\sigma} A_{\lambda})}$.