# Finding Taylor approximation for $x^4e^{-x^3}$

I'm trying to find Taylor approximation for the function: $$x^4e^{-x^3}$$

I started taking the first, second, third, etc. derivatives but the expression for it seems to explode with terms. I was just wondering is there a trick for this one or do I just have to use brute force in order to discover the pattern? :)

thnx for any help

Notice $$\exp(x) = \sum \frac{x^n}{n!} \implies \exp(-x^3) = \sum\frac{(-1)^nx^{3n}}{n!} \implies x^4 \exp(-x^3) = \sum\frac{(-1)^nx^{3n+4}}{n!}$$
• +1 @Citizen Thank you for your help :) I thought I might have to use the expansion for $e^x$ for this somehow :) thnx again! – jjepsuomi Oct 9 '13 at 8:31
• The first equality IS the Taylor expansion of $e^x$ around $0$. – Laurent LA RIZZA Mar 17 '15 at 6:47