  Triangular matrix rings are example of trivial extensions. In this article we
describe the Jordan superderivations of the trivial extensions and upper
triangular matrix rings. We deduce then that any Jordan superderivation of an
upper triangular matrix ring, under some conditions, is a derivation, and any
Jordan super-biderivation of a trivial extension, and hence an upper triangular
matrix ring, is a Jordan biderivation.
