I was reading Einsteins 1916 original paper on GR, the "The foundation of the general theory of relativity". There are some derivation that he did but I didn't quite understand. It would be nice if someone can give me some direction or some guidance on it.
Here is the link to the paper. http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdf
My question originated from chapter #18, from the derivation of equation (57). He says that we can get (57) by by multiplying partial derivative ∂g^μν/∂x_σ with equation (53), but I tried and didn't quite get it. I know that this (57) amounts to showing the left side of the multiplied (53) to be zero (or this is wrong?) but I can't get it. One idea is that it can be factorisation by product rule of derivation. By multiplying (53) by a partial derivative one get two first degree derivative in one term, and I cannot figure out how to factorise them into a degree one derivative by product rule.