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Math Help - Help with differential equation

  1. #1
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    Mar 2008
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    Question Help with differential equation

    Hey guys,

    I have the following differential equation

    <br />
\frac{d}{dx} (x^2 e^(-x))<br />

    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
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  2. #2
    Member
    Joined
    May 2008
    Posts
    106
    Hi Kimmy,

    I assume you mean
    <br />
\frac{d}{dx}(x^2e^{-x})

    have you met the product rule yet? it is for when u and v are functions of x
    <br />
\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
    <br />
\frac{d}{dx}(x^2e^{-x})=2xe^{-x}-x^2e^{-x}

    hope that helps
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  3. #3
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    Joined
    Mar 2008
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    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.
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