Question

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

Answer 1

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

I used this prop: $\;\;(f\times g)'=f'\timesg+f\times g'$

So it's true