Deriving the Limit of x^3e^(-x^2) as x Approaches Infinity

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Homework Statement



lim(x→∞)x^3 e^((-x)^2 )

Homework Equations


The Attempt at a Solution


So I tried taking a derivative as both, multiplication and a fraction. I make a mistake somewhere. I get a very complicated answer.
 
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OK, I solved it.
 

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