  We consider the unparticle action that is made gauge invariant by inclusion
of an open Wilson line factor. In deriving vertexes from such an action it has
been customary to use a form of differentiating the Wilson line originally
proposed by Mandelstam. Using a simple example, we show that the Mandelstam
derivative is mathematically inconsistent. We show that there are two ways to
define differentiation of the Wilson line. The mathematically consistent method
is to differentiate the explicit dependence of the line on the endpoint. The
other method is a functional derivative and corresponds in a limiting case to
the Mandelstam derivative. We also show that the only path that can be used in
the Wilson line integral that leaves the unparticle action both Poincare and
scale invariant is the straight line.
