We define a symmetric derivative on an arbitrary nonempty closed subset of the real numbers and derive some of its properties. It is shown that real-valued functions defined on time scales that are neither delta nor nabla differentiable can be symmetric differentiable.

This is a preprint of a paper whose final and definite form will be published in Applied Mathematics Letters. Submitted 30-Jul-2012; revised 07-Sept-2012; accepted 10-Sept-2012