  We provide a general framework to study differentiability of SRB measures for
one dimensional non-uniformly expanding maps. Our technique is based on
inducing the non-uniformly expanding system to a uniformly expanding one, and
on showing how the linear response formula of the non-uniformly expanding
system is inherited from the linear response formula of the induced one. We
apply this general technique to interval maps with a neutral fixed point
(Pomeau-Manneville maps) to prove differentiability of the corresponding SRB
measure. Our work covers systems that admit a finite SRB measure and it also
covers systems that admit an infinite SRB measure. In particular, we obtain a
linear response formula for both finite and infinite SRB measures. To the best
of our knowledge, this is the first work that contains a linear response result
for infinite measure preserving systems.
