How to find variation of a tensor quantity?

[niahl]

Hello! Forgive me if I sound amateur, but I'd like to know how one goes about finding the variation of tensor quantities. In the Einstein-Hilbert Action, variations of various quantities including the Riemannian Curvature are found. I'd like to know if there is some general rule to find the variation of any tensor.

 

[berkeman]

Welcome to the PF.

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