  We observed the interstellar comet 2I/Borisov using the Neil Gehrels-Swift
Observatory's Ultraviolet/Optical Telescope. We obtained images of the OH gas
and dust surrounding the nucleus at six epochs spaced before and after
perihelion (-2.56 AU to 2.54 AU). Water production rates increased steadily
before perihelion from $(7.0\pm1.5)\times10^{26}$ molecules s$^{-1}$ on Nov. 1,
2019 to $(10.7\pm1.2)\times10^{26}$ molecules s$^{-1}$ on Dec. 1. This rate of
increase in water production rate is quicker than that of most dynamically new
comets and at the slower end of the wide range of Jupiter-family comets. After
perihelion, the water production rate decreased to $(4.9\pm0.9)\times10^{26}$
molecules s$^{-1}$ on Dec. 21, which is much more rapidly than that of all
previously observed comets. Our sublimation model constrains the minimum radius
of the nucleus to 0.37 km, and indicates an active fraction of at least 55% of
the surface. $A(0)f\rho$ calculations show a variation between 57.5 and 105.6
cm with a slight trend peaking before the perihelion, lower than previous and
concurrent published values. The observations confirm that 2I/Borisov is
carbon-chain depleted and enriched in NH$_2$ relative to water.
