  We consider the linear and quadratic higher order terms associated to the
response of the statistical properties of a dynamical system to suitable small
perturbations. These terms are related to the first and second derivative of
the stationary measure with respect to the change of some parameters,
expressing how the statistical properties of the system varies under the
perturbation. We show a general framework in which one can obtain rigorous
convergence and formulas for these two terms. The framework is flexible enough
to be applied both to deterministic and random systems. We give examples of
such an application computing linear and quadratic response for Arnold maps
with additive noise and deterministic expanding maps.
