Let $ \ f(x) \ = \ x^4 e^x \ $ . Determine the nth derivative of $ \ f \ $ at $ \ x \ = \ 0 \ $.
I know by working it out that the first, second, and third derivative will be 1. The fourth, fifth, and onward derivatives will be 0.
However, the textbook answer is n(n-1)(n-2)(n-3). I'm having difficulty understanding this, because according to that formula, the first, second, and third derivative will all equal zero, or am I misinterpreting it somehow?