# Euler-Lagrange derivative for any Lagrangian density which is a function of Metric and its first and second derivatives

I know formalism of Euler_Lagrange derivatives:

which $$L$$ here is a Lagrangian density.

now I wonder how can I make such a form as below for any Lagrangian density which is a function of metric and its first and second derivatives?

My main problem is transforming the first two terms of Euler_Lagrange derivatives formalism to this shape.

• There is a cool derivation of almost the same in Carroll's book on GR... – user192234 Jul 19 at 9:46