  For asymptotically flat black holes, Reall-Santos method is a convenient tool
to compute leading higher derivative corrections to the thermodynamic
quantities without actually solving the modified field equations. However,
there are subtleties in its generalization to asymptotically AdS black holes
with general higher derivative corrections. First of all, it is necessary to
know all the higher derivative holographic counterterms and the surface terms
implementing the variational principle and subtracting the divergence. One then
needs to solve for the modified AdS radius and rescale the time coordinate in
an appropriate way such that the induced metric on the conformal boundary of
AdS black hole is not modified. We observe that Reall-Santos method can be
directly applied to a particular 4-derivative gravity model, known as the
Einstein-Weyl gravity, which does not modify the AdS radius and requires only
the Gibbons-Hawking-York term and holographic counterterms for the 2-derivative
theory. We thus suggest that to compute the thermodynamic quantities of AdS
black holes in general 4-derivative theories of gravity, one simply needs to
transform it to a Einstein-Weyl gravity with identical thermodynamic variables
by appropriate field redefinitions. We explicitly verify this proposal with
spherically-symmetric and static charged black holes in Einstein-Maxwell theory
extended with generic 4-derivative interactions.
