Christoffel connection

Question

I am trying to determine the correct expression when expanding a contravariant derivative acting on another contravariant derivative acting on the Ricci scalar.

$\nabla^a \nabla^b R = \partial^a \nabla^b R$ + Christoffel symbol x derivative of R

However I am not able to find a way to keep the indices in the correct place while still having one upper and two lower indices on the Christoffel symbol.

Answer 1

I realised the answer was to lower the derivatives using the metric first, then to expand out into partial + Christoffel symbol