theorem :: SIN_COS9:124

for Z being open Subset of REAL st Z c= ].(- 1),1.[ holds
( exp_R (#) arccot is_differentiable_on Z & ( for x being Real st x in Z holds
((exp_R (#) arccot) `| Z) . x = ((exp_R . x) * (arccot . x)) - ((exp_R . x) / (1 + (x ^2))) ) )