Question

How do you find the derivative of `f(x)=-xe^x + 2`?

Answer 1

`f'(x)=-e^x(x+1)`

Explanation:

differentiate `xe^x` using the `color(blue)"product rule"`

`"Given "y=g(x).h(x)" then"`

`• dy/dx=g(x)h'(x)+h(x)g'(x)`

`"here "g(x)=xrArrg'(x)=1`

`"and "h(x)=e^xrArrh'(x)=e^x`

`rArrf(x)=-xe^x+2`

`rArrf'(x)=-(x.e^x+e^x)+0=-xe^x-e^x`

`color(white)(rArrf'(x))=-e^x(x+1)`