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

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Answer 1 · 2016-06-15T19:44:34

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

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.

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