First and second derivatives (i.e L = L (gab, gab,c, gab,cd , xe))

PS: Aim of the question is to reach to the attached picture equation.

b) For the Ricci scalar, obtain dR/dgab,cd in terms of metric.

c) Mathematically, express how the functionality of R is in terms of the second derivative of metric.

d) By using the relation in picture, for the Einstein-Hilbert Lagrangian density, (i.e. LE.-H. = (√ -g )R, get (δLE.-H.)/δgab in terms of the Einstein tensor.