  A large extension of the Sextans dwarf spheroidal galaxy, 7 sq degrees, has
been surveyed for variable stars using the Dark Energy Camera at the Blanco
Telescope in Cerro Tololo Inter-American Observatory, Chile. We report 7
Anomalous Cepheids, 199 RR Lyrae stars and 16 dwarf Cepheids in the field. This
is only the fifth extra-galactic systems in which dwarf Cepheids have been
systematically searched. Henceforth, the new stars increase the census of stars
coming from different environments that can be used to asses the advantages and
limitations of using dwarf Cepheids as standard candles in populations for
which the metallicity is not necessarily known. The dwarf Cepheids found in
Sextans have a mean period of 0.066 days, and a mean $g$ amplitude of 0.87
mags. They are located below the horizontal branch spanning a range of 0.8 mag,
between $21.9 < g < 22.7$. The number of dwarf Cepheids in Sextans is low
compared with other galaxies such as Carina, which have a strong
intermediate-age population. On the other hand, the number and ratio of RR
Lyrae stars to dwarf Cepheids is quite similar to Sculptor, a galaxy which, as
Sextans, is dominated by an old stellar population. The dwarf Cepheid stars
found in Sextans follow a well constrained Period-Luminosity relationship with
an rms=0.05 mag in the $g$ band, which was set up by anchoring to the distance
modulus given by the RR Lyrae stars. Although the majority of the variable
stars in Sextans are located toward the center of the galaxy, we have found 2
RR Lyrae stars and 1 Anomalous Cepheid in the outskirts of the galaxy, which
may be extra-tidal stars and suggest this galaxy may be undergoing tidal
destruction. These possible extra-tidal variable stars share the same proper
motions as Sextans, as seen by recent Gaia measurements.
