for S, T being RealNormSpace
for x0 being Real
for g being PartFunc of REAL, the carrier of S st g is_differentiable_in x0 holds
for f being PartFunc of the carrier of S, the carrier of T st f is_differentiable_in g /. x0 holds
( f * g is_differentiable_in x0 & diff ((f * g),x0) = (diff (f,(g /. x0))) . (diff (g,x0)) )