theorem Th32: :: PDIFF_1:32

for m, n being non zero Nat
for i being Nat
for r being Real
for f being PartFunc of (REAL-NS m),(REAL-NS n)
for x being Point of (REAL-NS m) st f is_partial_differentiable_in x,i holds
( r (#) f is_partial_differentiable_in x,i & partdiff ((r (#) f),x,i) = r * (partdiff (f,x,i)) )