  In this small note, we establish Malliavin differentiability of McKean-Vlasov
Stochastic Differential Equations (MV-SDEs) with drifts satisfying both a
locally Lipschitz and a one-sided Lipschitz assumption, and where the diffusion
coefficient is assumed to be uniformly Lipschitz in its variables. As a
secondary contribution, we investigate how Malliavin differentiability
transfers across to the interacting particle system associated with the
McKean-Vlasov equation to its limiting equation. This final result requires
both spatial and measure differentiability of the coefficients and doubles as a
standalone result of independent interest since the study of Malliavin
derivatives of weakly interacting particle systems seems novel to the
literature.
