  A mathematical complication due to an unnecessary formal assumption
concerning the variational principle of general relativity theory, which
apparently bothered Einstein and Hilbert, is shown and cleared up. Some
historical confusion seems caused by the impossibility to use the conventional
Euler-Lagrange formalism directly there, which even otherwise is nothing but
one of various possible procedures to apply the superior principle of least
action. Correspondingly to the absence of any direct calculation in the
literature so far, only a numerical modification in parts - explicitly taken
into account now after once mentioned by Hilbert without implementation - would
allow to compute the fundamental Einstein tensor density from these authors'
initial formulae, which must not be taken literally. Nevertheless adhering to a
merely symbolic Euler-Lagrange formalism, this needs a clear distinction
between 'component differentiation' and 'tensor differentiation' defined here.
Various corresponding solutions are shown including the probably most natural
one. Two of them are additionally verified in the detailed supplementary
material appended to the electronic edition of the note.
