  We report on new NuSTAR and archival Chandra observations of the pulsar wind
nebula (PWN) 3C 58. Using the X-ray data, we measure energy-dependent
morphologies and spatially-resolved spectra of the PWN. We find that the PWN
size becomes smaller with increasing energy and that the spectrum is softer in
outer regions. In the spatially integrated spectrum of the PWN, we find a hint
of a spectral break at $\sim$25 keV. We interpret these findings using
synchrotron-radiation scenarios. We attribute the size change to the
synchrotron burn-off effect. The radial profile of the spectral index has a
break at $R\sim80''$, implying a maximum electron energy of $\sim$200 TeV which
is larger than a previous estimate, and the 25-keV spectral break corresponds
to a maximum electron energy of $\sim$140 TeV for an assumed magnetic field
strength of 80 $\mu$G. Combining the X-ray data and a previous radio-to-IR SED,
we measure a cooling break frequency to be $\sim 10^{15}$ Hz, which constrains
the magnetic-field strength in 3C 58 to be 30-200$\mu$G for an assumed age
range of 800-5000 years.
