theorem :: PDIFF_3:30

for r being Real
for z0 being Element of REAL 2
for f being PartFunc of (REAL 2),REAL st f is_hpartial_differentiable`12_in z0 holds
( r (#) (pdiff1 (f,1)) is_partial_differentiable_in z0,2 & partdiff ((r (#) (pdiff1 (f,1))),z0,2) = r * (hpartdiff12 (f,z0)) )