theorem Th11: :: NDIFF_4:11

for x0 being Real
for n being non zero Element of NAT
for f1, f2 being PartFunc of REAL,(REAL n) st f1 is_differentiable_in x0 & f2 is_differentiable_in x0 holds
( f1 + f2 is_differentiable_in x0 & diff ((f1 + f2),x0) = (diff (f1,x0)) + (diff (f2,x0)) )