17 Jun
2007
17 Jun
'07
4:58 p.m.
Marc wrote: << Is there term for when f(a b) = a f(b) + b f(a)? And the answer, supplied by Neil, is "derivation". Okay, sure, if say C^oo(R) is the set of infinitely differentiable functions from R to R, then D: C^oo(R) -> C^oo(R) defined by D(f)(x) = f'(x) is perhaps the epitome of a derivation. -------------------------------------------------------------------- But what are the continuous derivations d: R -> R ? I.e., for all real u,v, we must have d(uv) = d(u)*v + u*d(v) The 0 function works. What is the general solution? --Dan