  Recently, some problems have been found in the definition of the partial
derivative in the case of the presence of both explicit and implicit functional
dependencies in the classical analysis. In this talk we investigate the
influence of this observation on the quantum mechanics and classical/quantum
field theory. Surprisingly, some commutators of the coordinate-dependent
operators are not equal to zero. Therefore, we try to provide mathematical
foundations to the modern non-commutative theories. We also indicate possible
applications in the Dirac-like theories.
