theorem Th4: :: INTEGRA9:4

for n being Element of NAT st n <> 0 holds
( (- (1 / n)) (#) (cos * (AffineMap (n,0))) is_differentiable_on REAL & ( for x being Real holds (((- (1 / n)) (#) (cos * (AffineMap (n,0)))) `| REAL) . x = sin (n * x) ) )