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Math Help - Derivative help?.. again

  1. #1
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    Derivative help?.. again

    F(y)=(\frac{1}{y^2}-\frac{3}{y^4})(y+5y^3)

    I'm not sure where to start so I tried to get rid of the fraction.
    <br />
(y^4)(\frac{1}{y^2}-\frac{3}{y^4})(y+5y^3)
    =(y^2-3)(y^5+5y^7)
    now I differentiated
    (2y-0)(y^5+5y^7)+(y^2-3)(5y^4+35y^6)
    which turns into a ridiculously large.. and wrong answer after i simplify <br />
45y^8-38y^6-15y^4

    book's answer is <br />
5+\frac{14}{y^2}+\frac{9}{y^4}
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  2. #2
    MHF Contributor matheagle's Avatar
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    you also must divide by y^4
    the derivative of f(y) is not the same as y^4f(y)
    Just multiply the original function and differentiate term by term, and don't use the product rule.
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  3. #3
    Super Member bigwave's Avatar
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    Quote Originally Posted by dorkymichelle View Post
    F(y)=(\frac{1}{y^2}-\frac{3}{y^4})(y+5y^3)

    I'm not sure where to start so I tried to get rid of the fraction.
    <br />
(y^4)(\frac{1}{y^2}-\frac{3}{y^4})(y+5y^3)
    =(y^2-3)(y^5+5y^7)
    now I differentiated
    (2y-0)(y^5+5y^7)+(y^2-3)(5y^4+35y^6)
    which turns into a ridiculously large.. and wrong answer after i simplify <br />
45y^8-38y^6-15y^4

    book's answer is <br />
5+\frac{14}{y^2}+\frac{9}{y^4}
    on way to get rid of fractions is to inverse the exponents
    f(y) = (y^{-2}-3y^{-4})(y+5y^{3})
    then FOIL it
    f (y) = y^{-1}+5y-3y^{-3}-15y^{-1}<br />
\Rightarrow<br />
5y-14y^{-1}-3y^{-3}
    so then f'(y) = 5+14y^{-2}+9y^{-4}\Rightarrow5+\frac{14}{y^2}+\frac{9}{y^4}
    Last edited by bigwave; March 15th 2010 at 12:57 AM.
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  4. #4
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    So I don't use the multiplication derivative rule?
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  5. #5
    Super Member bigwave's Avatar
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    Cool rewrite expression into terms

    i would agree with matheagle that you can use the product or quotient rule
    but it is much more efficient to rewrite your expression into just terms and take the derivative from there.

    (f \cdot g)' =  f \cdot g'+g \cdot f'

    and

     \left(\frac{f}{g}\right)' = \frac{g \cdot f'-f \cdot g'}{g^2}

    would be quite involved with this problem

    hope this helps.
    Last edited by bigwave; March 15th 2010 at 03:28 PM. Reason: latex
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  6. #6
    MHF Contributor matheagle's Avatar
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    I would just use the power rule as wavelet did
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