theorem :: PDIFF_4:39

for s, t being Real
for p being Element of REAL 3
for f, g being PartFunc of (REAL 3),REAL st f is_partial_differentiable_in p,1 & f is_partial_differentiable_in p,2 & f is_partial_differentiable_in p,3 & g is_partial_differentiable_in p,1 & g is_partial_differentiable_in p,2 & g is_partial_differentiable_in p,3 holds
grad (((s (#) f) - (t (#) g)),p) = (s * (grad (f,p))) - (t * (grad (g,p)))