  This investigation pertains to the construction of a class of generalised
deformed derivative operators which furnish the familiar finite difference and
the q-derivatives as special cases. The procedure involves the introduction of
a linear operator which is multiplicative over functions of a real variable.
The validity of the general prescriptions is ascertained by considering
suitable examples of such derivatives and constructing their eigenfunctions
explicitly. The relationship of a particular version of the operator with the
one-dimensional Mobius transformation is also established.
