  We study the Planck CMB temperature at different scales through its
derivatives up to second order, which allows one to characterize the local
shape and isotropy of the field. The problem of having an incomplete sky in the
calculation and statistical characterization of the derivatives is addressed in
the paper. The analysis confirms the existence of a low variance in the CMB at
large scales, which is also noticeable in the derivatives. Moreover, deviations
from the standard model in the gradient, curvature and the eccentricity tensor
are studied in terms of extreme values on the data. As it is expected, the Cold
Spot is detected as one of the most prominent peaks in terms of curvature, but
additionally, when the information of the temperature and its Laplacian are
combined, another feature with similar probability at the scale of $10^\circ$
is also observed. However, the $p$-value of these two deviations increase above
the $6\%$ when they are referred to the variance calculated from the
theoretical fiducial model, indicating that these deviations can be associated
to the low variance anomaly. Finally, an estimator of the directional
anisotropy for spinorial quantities is introduced, which is applied to the
spinors derived from the field derivatives. An anisotropic direction whose
probability is $<1\%$ is detected in the eccentricity tensor.
