# Thread: Help with differential equation

1. ## Help with differential equation

Hey guys,

I have the following differential equation

$
\frac{d}{dx} (x^2 e^(-x))
$

but i dont know how to differentiate it. So could someone please help, showing me the exact steps so i know how to do this for future questions.

Thank you in advance for any help

2. Hi Kimmy,

I assume you mean
$
\frac{d}{dx}(x^2e^{-x})$

have you met the product rule yet? it is for when u and v are functions of x
$
\frac{d}{dx}(uv)=u\frac{dv}{dx}+v\frac{du}{dx}$

so in this case you would have $u=x^2$ and $v=e^{-x}$

which would give $\frac{du}{dx}=2x$ and $\frac{dv}{dx}=-e^{-x}$

so using the above rule we get
$
\frac{d}{dx}(x^2e^{-x})=2xe^{-x}-x^2e^{-x}$

hope that helps

3. Yeah have used that before. Thanks alot. Now i know the method i should be able to solve any questions i come across now.

Thanks again.