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Math Help - Another derivative

  1. #1
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    Another derivative

    Hi,

    I'm not sure what rules I'd use to solve down this derivative and how I'd go about employing these rules.

    I need to find the derivative of:

    f(x)=(x^5-3x)(\frac{1}{x^2})

    If you can guide me that would be excellent. Thank you.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    If f(x)=x^n
    f'(x)=nx^{n-1}

    f(x)=x^3-\frac{3}{x}
    f'(x)=3x^2+\frac{3}{x^2}
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jimmyp View Post
    Hi,

    I'm not sure what rules I'd use to solve down this derivative and how I'd go about employing these rules.

    I need to find the derivative of:

    f(x)=(x^5-3x)(\frac{1}{x^2})

    If you can guide me that would be excellent. Thank you.
    You could use the product rule, but it's easier just to multiply out and use the power rule. like so:


    \frac{d}{dx}[(x^5-3x)(\frac{1}{x^2})]=\frac{d}{dx}[(x^{-2})(x^5-3x)]=\frac{d}{dx}[(x^{5+(-2)}-3x^{1+(-2)}]

    =\frac{d}{dx}[x^{3}-3x^{-1}]=3x^{2}+3x^{-2}=3x^2+\frac{3}{x^2}
    Last edited by VonNemo19; May 28th 2009 at 09:44 PM. Reason: messed up bad
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