  A symmetric function of $N$ variables can be given in terms of symmetric
polynomials of these variables. We determine those symmetric polynomials in
which the dual differential operators take the neatest form when expressed in
terms of our original variables, producing a simple form for the associated
Weyl algebra. Both our coordinates, and the form of our differential operators
at total diagonal points, exhibit interesting properties, and are related to
interesting objects like Bell polynomials. They can be modified to give a
simple formula for the gradient of our symmetric function at any point.
