theorem :: FDIFF_11:4

for Z being open Subset of REAL st Z c= dom (arccot * cos) & ( for x being Real st x in Z holds
( cos . x > - 1 & cos . x < 1 ) ) holds
( arccot * cos is_differentiable_on Z & ( for x being Real st x in Z holds
((arccot * cos) `| Z) . x = (sin . x) / (1 + ((cos . x) ^2)) ) )