Derivatives in Noncommutative calculus and deformation property of quantum algebras

The aim of my talk is twofold. First, I introduce analogs of (partial) derivatives on certain Noncommutative algebras, including some enveloping algebras and their "braided versions". Second, I discuss deformation property of some quantum algebras and show that contrary to a commonly held view the so-called "q-Witt algebra" does not have a good deformation property (i.e. it is not a deformation of its classical counterpart).