  We extend some definitions and give new results about the theory of slice
analysis in several quaternionic variables. The sets of slice functions which
are respectively slice, slice regular and circular w.r.t. given variables are
characterized. We introduce new notions of partial spherical values and
derivative for functions of several variables that extend those of one
variable. We recover some of their properties and find new ones. Finally, we
prove a generalization of Fueter's Theorem in this context.
