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What is a function whose derivative is 2xe^{{x2}}?

Rearrange this a little.

2xe^{{x2}} = e^{{x2}} × (2x).

If we let u = x^{2}, then u' = 2x and therefore e^{{x2}} × (2x) = e^{u} × u' .

What function has a derivative of e^{u} × u'? e^{u}. Our answer is e^{u}, or e^{{x2}}.

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