How might one find the divergence of a second order (stress) tensor?

I'm pretty sure it's zero here thanks to the momentum balance equation. But I need to expand it so I can pull out an ODE, but I know next to zilch about tensors.

Like how do I calculate it based on the tensor elements? I think in my coordinate system only the diagonal elements of the tensor are non-zero.

I don't really understand tensor index notation very well.