theorem :: EUCLID_8:105

for r being Real
for f1, f2, f3, g1, g2, g3 being PartFunc of REAL,REAL
for t0 being Real st f1 is_differentiable_in t0 & f2 is_differentiable_in t0 & f3 is_differentiable_in t0 & g1 is_differentiable_in t0 & g2 is_differentiable_in t0 & g3 is_differentiable_in t0 holds
VFuncdiff ((r (#) (f1 + g1)),(r (#) (f2 + g2)),(r (#) (f3 + g3)),t0) = (r * (VFuncdiff (f1,f2,f3,t0))) + (r * (VFuncdiff (g1,g2,g3,t0)))