2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129708Analysing an application in liquid film dynamics, a guide for obtaining the corresponding constrained functional derivatives for constraints coupling the functional variables is given. The use of constrained derivatives makes the proper account for constraints possible in time-dependent, nonequilibrium physical theories, with physical equations not emerging as Euler-Lagrange equations, which is especially relevant with respect to the dynamics of complex liquids.12 pages; with further cases of coupling added, extended opening discussion of constrained derivative, and some notation changedFluid DynamicsMathematical PhysicsFunctional Analysistext