  We obtain integral representations of the $n$-th derivatives of the Bessel
functions with respect to the order. The numerical evaluation of these
expressions is very efficient using a double exponential integration strategy.
Also, from the integral representation corresponding to the Macdonald function,
we have calculated a new integral. Finally, we calculate integral expressions
for the fractional derivatives of the Bessel functions with respect to the
order. Simple proofs for some particular cases given in the literature are
provided as well.
