A common replacement of the tangent space to a noncommutative space whose
coordinate algebra is the enveloping algebra of a Lie algebra is generated by
the deformed derivatives, usually defined by procedures involving orderings
among noncommutative coordinates. We show that an approach to extending the
noncommutative configuration space to a phase space, based on a variant of
Heisenberg double, more familiar for some other algebras, e.g. quantum groups,
is in the Lie algebra case equivalent to the approach via deformed derivatives.
The dependence on the ordering is now in the form of the choice of a suitable
linear isomorphism between the full algebraic dual of the enveloping algebra
and a space of formal differential operators of infinite order.