There are some differences between art. 110.14(C) and 310.15(B)(3)
310.15 Ampacities for Conductors Rated 0–2000 Volts.(B) Tables:
The temperature correction and adjustment factors shall be permitted to be applied to the ampacity for the temperature rating of the conductor, if the corrected and adjusted ampacity does not exceed the ampacity for the temperature rating of the termination in accordance with the provisions of 110.14(C).
What “ampacity”?
110.14(C) Temperature Limitations. The temperature rating associated with the ampacity of a conductor shall be selected and coordinated so as not to exceed the lowest temperature rating of any connected termination, conductor, or device.
Conductors with temperature ratings higher than specified for terminations shall be permitted to be used for ampacity adjustment, correction, or both.
Because we design power plants we do not use tables but calculate the ampacity.
In art.310.15(C) Engineering Supervision it is the formula:
I=√(Tc-Ta)/(Rdc(1+Yc)Rca)
Following Neher & McGrath and IEEE 835 we start with the rated conductor temperature [let’s say 90oC]
If we follow IEEE 835/1994 Annex A number of conductors is built-in Rca formula:
Rca=Ri+n(Rj+Rsd+Rc+Re) where:
Ri insulation thermal resistance [T.O.F.]
Rj jacket thermal resistance
Rsd =Cable to conduit
Rc=Conduit wall
Re=is thermal resistance of the earth or external thermal circuit (air, duct bank, etc.)
n=number of conductors within a stated diameter[Neher & McGrath Nomenclature]
That means-in my opinion- the derating purpose it is to adjust the ampacity in order to keep conductor temperature at 90oC.[it is not in order to reduce the conductor temperature].