  The one loop UV divergences of Hilbert-Einstein gravity with a cosmological
constant and spin 0, 1/2 and 1 matter are computed making use of a covariant
derivative expansion and functional methods. For this purpose the
transformation that yields the covariant derivative is extended to include a
dynamical metric and the expansion in the fields themselves is made covariant
which is relevant for the effective action due to the non-linear character of
gravity
