How does derivation of Lagrange equation from d’Alembert principle differ from the derivation of it from principle of least action?

Question

Using d’Alembert principle, one doesn't require any assumption like the one made in other case where particle has to follow the path of least action.

Answer 1

First and foremost, the generalized forces $Q_j$ do need to have (possibly velocity-dependent) potentials for the stationary action principle to work, while this is not necessary for d'Alembert's principle. See also this & this related Phys.SE posts.