In this paper a type of path derivative, which is not based on the non-empty path intersection, is introduced. Such derivatives share some basic properties with sequencial derivatives but there exist some sharp contrasts between them. The path derivative here restricts the speed of convergence in the definition of limits naturally and has a sharp contrast with the classical Dini derivatives for the typical continuous function.
"A type of path derivative.." Real Anal. Exchange 28 (2) 279 - 286, 2002/2003.