theorem :: FDIFF_11:2

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