  We continue the development of the basic theory of generalized derivatives as
introduced in \cite{JPA} and give some of their applications. In particular, we
formulate versions of a weak maximum principle, Rolle's theorem, the Mean value
theorem, the Fundamental theorem of Calculus, Integration by parts, along with
an existence and uniqueness theorem for a generalized Riccati equation, each of
which includes, as corollaries, the corresponding version for conformable
fractional derivatives considered by \cite{kat}, \cite{kha} among many others.
Finally, we show that for each $\alpha > 1$ there is a fractional derivative
and a corresponding function whose fractional derivative fails to exist
everywhere on the real line.
