Protoplanetary disks emit radiation across a broad range of wavelengths, requiring a multiwavelength approach to fully understand their physical mechanisms and how they form planets. Observations at submillimeter to centimeter wavelengths can provide insights into the thermal emission from dust, free-free emission from ionized gas, and possible gyro-synchrotron emission from the stellar magnetosphere. This work is focused on CX Tau, a ~0.4 M_⊙ star with an extended gas emission and a compact and apparently structureless dust disk, with an average millimeter flux compared to Class II sources in Taurus. We present observations from the Karl G. Jansky Very Large Array across four bands (between 9.0 mm and 6.0 cm) and combine them with archival data from the Atacama Large Millimeter/submillimeter Array, the Submillimeter Array, and the Plateau de Bure Interferometer. This multiwavelength approach allows us to separate the dust continuum from other emissions. After isolating the dust thermal emission, we derived an upper limit of the dust disk extent at 1.3 cm, which is consistent with theoretical predictions of a radial drift-dominated disk. The centimeter data show a peculiar behavior: deep observations at 6.0 cm did not detect the source, while at 1.3 cm, the flux density is anomalously higher than adjacent bands. Intraband spectral indices suggest a dominant contribution from free-free emission, whereas gyro-synchrotron emission is excluded. To explain these observations, we propose a strong variability among the free-free emission with timescales shorter than a month. Another possible interpretation is the presence of anomalous microwave emission from spinning dust grains.