  Generalized symmetries and supersymmetries depending on derivatives of
dynamic variables are treated in a most general setting. Studding cohomology of
the variational bicomplex, we state the first variational formula and
conservation laws for Lagrangian systems on fiber bundles and graded manifolds
under generalized symmetries and supersymmetries of any order. Cohomology of
nilpotent generalized supersymmetries are obtained.
