  The model of kappa-deformed space is an interesting example of a
noncommutative space, since it allows a deformed symmetry.
  In this paper we present new results concerning different sets of derivatives
on the coordinate algebra of kappa-deformed Euclidean space. We introduce a
differential calculus with two interesting sets of one-forms and higher-order
forms. The transformation law of vector fields is constructed in accordance
with the transformation behaviour of derivatives. The crucial property of the
different derivatives, forms and vector fields is that in an n-dimensional
spacetime there are always n of them. This is the key difference with respect
to conventional approaches, in which the differential calculus is
(n+1)-dimensional.
  This work shows that derivative-valued quantities such as derivative-valued
vector fields appear in a generic way on noncommutative spaces.
