Question

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

Answer 1

`(d)/(dx)\left(xe^(x)\right)=(d)/(dx)(x)* e^x+x*(d)/(dx)\left(e^x\right)\\\\=1* e^x+xe^x\\\\=e^x+xe^x\\\\Factorised:\\=e^x(x+1)`

I used this prop:
`\;\;(f* g)'=f'*g+f* g'`

So it's true