Question

How do you find the derivative of `x^2 * e^-x`?

Answer 1

`d/dx(x^2*e^-x)=2xe^-x-x^2e^-x`

Explanation:

This problem requires use of the product rule, which states:
`d/dx(uv)=u'v+uv'`
Where `u` and `v` are functions of `x`.

In our case, `u=x^2->u'=2x` and `v=e^(-x)->v'=-e^(-x)`. Thus
`d/dx(x^2*e^-x)=(2x)(e^-x)+(x^2)(-e^-x)`
`=2xe^-x-x^2e^-x`

We could simplify this a little further by, say, pulling out an `xe^-x`:
`d/dx(x^2*e^-x)=xe^-x(2-x)`

Either form is correct.