theorem :: FDIFF_7:50

for Z being open Subset of REAL
for f being PartFunc of REAL,REAL st Z c= dom ((sin / cos) * f) & ( for x being Real st x in Z holds
( f . x = x / 2 & cos . (f . x) <> 0 ) ) holds
( (sin / cos) * f is_differentiable_on Z & ( for x being Real st x in Z holds
(((sin / cos) * f) `| Z) . x = 1 / (1 + (cos . x)) ) )