There are many results on the simultaneous approximation by sequences of
special positive linear operators. In the year 1978, Ismail and May as well as
Volkov independently studied operators of exponential type covering the most
classical approximation operators. In this paper we study asymptotic properties
of these class of operators. We prove that under certain conditions, asymptotic
expansions for sequences of operators belonging to a slightly larger class of
operators, can be differentiated term-by-term. This general theorem contains
several results which were previously obtained by several authors for concrete
operators. One corollary states, that the complete asymptotic expansion for the
Bernstein polynomials can be differentiated term-by-term. This implies a
well-known result on the Voronovskaja formula obtained by Floater