  We produce uniform and decaying bounds in time for derivatives of the
solution to the backwards Kolmogorov equation associated to a stochastic
processes governed by a time dependent dynamics. These hold under assumptions
over the integrability properties in finite time of the derivatives of the
transition density associated to the process, together with the assumption of
remaining close over all $[0,\infty)$, or decaying in time, to some static
measure. We moreover provide examples which satisfy such a set of assumptions.
Finally, the results are interpreted in the McKean-Vlasov context for monotonic
coefficients by introducing an auxiliary non-autonomous stochastic process.
