theorem Th67: :: FDIFF_11:67

for Z being open Subset of REAL st Z c= ].(- 1),1.[ & ( for x being Real st x in Z holds
arctan . x <> 0 ) holds
( arctan ^ is_differentiable_on Z & ( for x being Real st x in Z holds
((arctan ^) `| Z) . x = - (1 / (((arctan . x) ^2) * (1 + (x ^2)))) ) )