theorem :: FDIFF_4:54

for n being Element of NAT
for Z being open Subset of REAL st Z c= dom ((1 / n) (#) ((#Z n) * sin)) & n > 0 holds
( (1 / n) (#) ((#Z n) * sin) is_differentiable_on Z & ( for x being Real st x in Z holds
(((1 / n) (#) ((#Z n) * sin)) `| Z) . x = ((sin . x) #Z (n - 1)) * (cos . x) ) )