theorem Th27: :: FDIFF_4:27

for a being Real
for Z being open Subset of REAL
for f being PartFunc of REAL,REAL st Z c= dom ((#R (3 / 2)) * f) & ( for x being Real st x in Z holds
( f . x = a + x & f . x > 0 ) ) holds
( (#R (3 / 2)) * f is_differentiable_on Z & ( for x being Real st x in Z holds
(((#R (3 / 2)) * f) `| Z) . x = (3 / 2) * ((a + x) #R (1 / 2)) ) )