theorem
for
z0 being
Element of
REAL 2
for
f1,
f2 being
PartFunc of
(REAL 2),
REAL st
f1 is_hpartial_differentiable`22_in z0 &
f2 is_hpartial_differentiable`22_in z0 holds
(
(pdiff1 (f1,2)) + (pdiff1 (f2,2)) is_partial_differentiable_in z0,2 &
partdiff (
((pdiff1 (f1,2)) + (pdiff1 (f2,2))),
z0,2)
= (hpartdiff22 (f1,z0)) + (hpartdiff22 (f2,z0)) )