theorem Th85: :: SIN_COS9:85

for x being Real
for f being PartFunc of REAL,REAL st f is_differentiable_in x & f . x > - 1 & f . x < 1 holds
( arctan * f is_differentiable_in x & diff ((arctan * f),x) = (diff (f,x)) / (1 + ((f . x) ^2)) )