Question

What is the derivative of `x^2 x e^-x`?

Answer 1

`3x^2e^-x-x^3e^-x`

Explanation:

Given: `x^2xe^-x`.

`=x^3e^-x`

We use the product rule, which states that,

`d/dx(xy)=yd/dx(x)+xd/dx(y)`

`:.dy/dx(x^3e^-x)=e^-xd/dx(x^3)+x^3d/dx(e^-x)`

`=e^-x*3x^2+x^3*-e^-x`

`=3x^2e^-x-x^3e^-x`