  The X-ray emission from active galactic nuclei (AGN) is believed to come from
a combination of inverse Compton scattering of photons from the accretion disk
and reprocessing of the direct X-ray emission by reflection. We present hard
(10-80 keV) and soft (0.5-8 keV) X-ray monitoring of a gravitationally lensed
quasar RX J1131-1231 with NuSTAR, Swift, and XMM-Newton between 10 June 2016
and 30 November 2020. Comparing the amplitude of quasar microlensing
variability at the hard and soft bands allows a size comparison, where larger
sources lead to smaller microlensing variability. During the period between 6
June 2018 and 30 November 2020, where both the hard and soft light curves are
available, the hard and soft bands varied by factors of 3.7 and 5.5,
respectively, with rms variability of $0.40\pm0.05$ and $0.57\pm0.02$. Both the
variability amplitude and rms are moderately smaller for the hard X-ray
emission, indicating that the hard X-ray emission is moderately larger than the
soft X-ray emission region. We found the reflection fraction from seven joint
hard and soft X-ray monitoring epochs is effectively consistent with a constant
with low significance variability. After decomposing the total X-ray flux into
direct and reprocessed components, we find a smaller variability amplitude for
the reprocessed flux compared to the direct emission. The power-law cutoff
energy is constrained at 96$^{+47}_{-24}$ keV, which position the system in the
allowable parameter space due to the pair production limit.
