  We extend some recent results on the differentiability of torsion theories.
In particular, we generalize the concept of $(\alpha, \beta)$-derivation to
$(\alpha, \beta)$-higher derivation and demonstrate that a filter of a
hereditary torsion theory that is invariant for $\alpha$ and $\beta$ is
$(\alpha, \beta)$-higher derivation invariant. As a consequence, any higher
derivation can be extended from a module to its module of quotients. Then, we
show that any higher derivation extended to a module of quotients extends also
to a module of quotients with respect to a larger torsion theory in such a way
that these extensions agree. We also demonstrate these results hold for
symmetric filters as well. We finish the paper with answers to two questions
posed in [L. Va\s, Extending higher derivations to rings and modules of
quotients, International Journal of Algebra, 2 (15) (2008), 711--731]. In
particular, we present an example of a non-hereditary torsion theory that is
not differential.
