theorem :: SIN_COS9:120

for Z being open Subset of REAL st Z c= dom (exp_R * arccot) & 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 . (arccot . x)) / (1 + (x ^2))) ) )