1. The problem statement, all variables and given/known data Say I had a problem like this: Prove that the nth derivative of x*e^(x) is (x+n)*e^(x) for all integer n. Can I use reverse induction to prove for negative n? For example... Say I proved it for my base case, n=0. In this case, the proof is trivial. Then I prove that if the nth derivative is (x+n)e^(x), then the (n+1)th derivative is (x+n+1)e^(x). (I didn't provide the proof because there's a similar homework problem here, and the proof is easy anyway. Can I then use reverse induction to prove that if the nth derivative is (x+n)e^(x), then the (n-1)th derivative is (x+n-1)e^(x), thus extending this case to negative derivatives (i.e., integrals)? Am I even making sense?