# math

what is the 3rd derivative of f(x)=x^2 e^x^2

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1. let me see what you got for the first derivative, so I can see if you are on the right track.

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2. 2x e^x^2+x^2 ex^2

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3. no, you have a product rule

y = (x^2)(e^(x^2))
y' = (x^2)(2x)(e^(x^2)) + (e^(x^2)) (2x)
now factor this
y' = (2x)(e^(x^2)) (x^2 + 1)
now you have triple product, so

y'' = (2x)(e^(x^2)) (2x) + (2x)(x^2 + 1)(2x(e^(x^2)) + 2(e^(x^2)) (x^2 + 1)
= 2 e^(x^2) (2x^2 + 2x^2(x^2+1) + (x^2 + 1) )
= 2 e^(x^2) (5x^2 + 2x^4 + 1)

now carefully do it once more

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