  We explore the radial variation of star formation histories in dwarf galaxies
simulated with Feedback In Realistic Environments (FIRE) physics. The sample
contains 9 low-mass field dwarfs with M_ star = 10^5 - 10^7 M_sun from previous
FIRE results, and a new suite of 17 higher mass field dwarfs with M_star = 10^7
- 10^9 M_sun introduced here. We find that age gradients are common in our
dwarfs, with older stars dominant at large radii. The strength of the gradient
correlates with overall galaxy age such that earlier star formation produces a
more pronounced gradient. The relation between formation time and strength of
the gradient is driven by both mergers and star-formation feedback. Mergers can
both steepen and flatten the age gradient depending on the timing of the merger
and star formation history of the merging galaxy. In galaxies without
significant mergers, early feedback pushes stars to the outskirts at early
times. Interestingly, among galaxies without mergers, those with large dark
matter cores have flatter age gradients because these galaxies have more
late-time feedback. If real galaxies have age gradients as we predict, stellar
population studies that rely on sampling a limited fraction of a galaxy can
give a biased view of its global star formation history. We show that central
fields can be biased young by a few Gyrs while outer fields are biased old.
Fields positioned near the 2D half-light radius will provide the least biased
measure of a dwarf galaxy's global star formation history.
