derivate x^4/e^x

Derivative

d/dx(x^4/e^x) = -e^(-x) (x - 4) x^3

Series expansion at x=0

4 x^3 - 5 x^4 + 3 x^5 - (7 x^6)/6 + x^7/3 + O(x^8)
(Taylor series)