theorem
for
u0 being
Element of
REAL 3
for
f1,
f2 being
PartFunc of
(REAL 3),
REAL st
f1 is_hpartial_differentiable`13_in u0 &
f2 is_hpartial_differentiable`13_in u0 holds
(
(pdiff1 (f1,1)) + (pdiff1 (f2,1)) is_partial_differentiable_in u0,3 &
partdiff (
((pdiff1 (f1,1)) + (pdiff1 (f2,1))),
u0,3)
= (hpartdiff13 (f1,u0)) + (hpartdiff13 (f2,u0)) )