Order of derivation if calculus of variation

Question

In reading the derivation of the relativistic free particle (covariant) equation of motion by extremising the relativistic action $-mc\int_A^B \, ds$, I stumbled upon a passage where the author inverts the order of the $d$ (derivation) and $\delta$ (variation) symbols: $d(\delta x^{\mu})= \delta (dx^{\mu})$, how is that possible? Given that the symbol $\delta x^{\mu}$ should represent an infinitesimal function (a variation) so it shouldn't even make sense to separate the two symbols.