[math-fun] term for f(a b) = a f(b) + b f(a)?

A function f when satisfying f(a b) = f(a) f(b) is described as "multiplicative". Is there term for when f(a b) = a f(b) + b f(a)? If not, what would you suggest? (I was thinking of saying "derivative", but maybe that's too confusing?) Thanks!