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.
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