Prefix operator with built-in evaluation rules.
is by default interpreted as D[y, x].
is used in mathematics to indicate boundary.
d gives \[Delta], not \[PartialD].
You can use \[InvisibleComma] in the subscript to to give several variables without having them separated by visible commas.
See The Mathematica Book: Section 1.10.4, Section 1.10.4, Section 3.10.3 and Section 3.10.4.
See also: \[Delta] , \[Del] , \[DifferentialD] , \[Eth] .