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Math Help - Product and Quotient Rule with Derivatives

  1. #1
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    Product and Quotient Rule with Derivatives

    The problem is:
    F(x) = ((1/y^2) - (2/y^4)) (y + 8y^3)

    I can find derivatives from other functions, but my professor has neglected to tell us how to do it with functions like this. I have tried this problem many times, with varying answers: It is so frustrating. I have used the product rule right away, or I have multiplied it out first and then used to power rule to find f'(x), but I keep getting the wrong answer. Please explain how to get the right answer and walk me through the question step by step. Thank you so much.
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  2. #2
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    f(x) = (\frac{1}{y^2} - \frac{2}{y^4})(y + 8y^3)

    =(y^{-2}-2y^{-4})*(y+8y^3)

    =y^{-1}+8y-2y^{-3}+16y^{-1}

    Well now you can use power rule on this:

    So f'(x)=(-1)*y^{-1-1}+8-2*(-3)y^{-3-1}+16*(-1)y^{-1-1}

    =-y^{-2}+6y^{-4}-16y^{-2}+8

    oh crap I misread a parenthesis. (fixing that now)

    There that's it.
    Last edited by seld; September 17th 2009 at 06:38 PM. Reason: messed up
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