theorem :: PDIFF_5:65

for r being Real
for u0 being Element of REAL 3
for f being PartFunc of (REAL 3),REAL st f is_hpartial_differentiable`32_in u0 holds
( r (#) (pdiff1 (f,3)) is_partial_differentiable_in u0,2 & partdiff ((r (#) (pdiff1 (f,3))),u0,2) = r * (hpartdiff32 (f,u0)) )