  The average R(t) of a smooth function with respect to the SRB measure of a
smooth one-parameter family f_t of piecewise expanding interval maps is not
always Lipschitz. We prove that if f_t is tangent to the topological class of
f_0, then R(t) is differentiable at zero, and the derivative coincides with the
resummation previously proposed by the first named author of the (a priori
divergent) series given by Ruelle's conjecture.
