At http://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/ar/ar2012/ar2012_352.pdf?__blob=publicationFile&v=1 page 80 it is stated: "The LOD for the combination are derived directly from the UT1–UTC data. The analytical expression for the first derivative of a cubic spline passing through the UT1–UTC data is used to estimate the LOD at the epoch of the UT1–UTC data."
At http://www.physics.arizona.edu/~restrepo/475A/Notes/sourcea-/node35.html#fg.spline bottom, left figure, in the part of domain -1 to -0.7 and near -0.5 tangent lines to original curve and to the curve made by cubic spline, make great angles. It means great difference in trigonometric tangents that are first derivatives.
In general for some parts of the domain of any function, first derivatives of the function obtained by cubic spline from the original, are severely deferent than first derivatives corresponding to original function.
Cubic spline although is good for find values of dependent variable, is bad for find first derivatives.
My question: Is IERS/Rapid Service/Prediction Centre wrong?