theorem :: PDIFF_3:31

for r being Real
for z0 being Element of REAL 2
for f being PartFunc of (REAL 2),REAL st f is_hpartial_differentiable`21_in z0 holds
( r (#) (pdiff1 (f,2)) is_partial_differentiable_in z0,1 & partdiff ((r (#) (pdiff1 (f,2))),z0,1) = r * (hpartdiff21 (f,z0)) )