  Motivated by recent experiments by Basov {\it et al}, we study the
differential sum rule for the effective scattering rate $1/\tau (\omega)$. We
show that in a dirty BCS superconductor, the area under $1/\tau (\omega)$ does
not change between the normal and the superconducting states.
  For magnetically mediated pairing, similar result holds between $T<T_c$ and
$T \geq T_c$, while in the pseudogap phase,
  $1/\tau (\omega)$ is just suppressed compared to $1/\tau(\omega)$ in the
normal state. We argue that this violation of the differential sum rule is due
to the fact that low-energy fermions in the pseudogap phase are still
incoherent.

Superconductivity;Strongly Correlated Electrons