theorem :: FDIFF_11:7

for Z being open Subset of REAL st Z c= dom (arctan * cot) & ( for x being Real st x in Z holds
( cot . x > - 1 & cot . x < 1 ) ) holds
( arctan * cot is_differentiable_on Z & ( for x being Real st x in Z holds
((arctan * cot) `| Z) . x = - 1 ) )