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15-04-2018
Mathematics

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Is the following true or false? d/dx[xe^x]=e^x(x+1)

Respuesta :

15-04-2018

[tex]\dfrac{d}{dx}\left(xe^{x}\right)=\dfrac{d}{dx}(x)\times e^x+x\times\dfrac{d}{dx}\left(e^x\right)\\\\=1\times e^x+xe^x\\\\=e^x+xe^x\\\\Factorised:\\=e^x(x+1)[/tex]

I used this prop: [tex]\;\;(f\times g)'=f'\timesg+f\times g'[/tex]

So it's true

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