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Math Help - Product Rule Error

  1. #1
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    Exclamation Product Rule Error

    Why do I get different answers when doing this?
    Take, for example, this equation:

    y = (x^3)/3 + 1/4x; the derivative would then be y' = x^2 + 1/4.

    But, if we were to re-write the equation by taking out an x, finding the derivative using the product rule gives you different answer.

    y = (x^3)/3 + 1/4x
    y = x((x^2)/3 + 1/4)
    y' = 1((x^2)/3 + 1/4) + x(x/6)
    y' = (x^2)/3 + 1/4 + (x^2)/6
    y' = (x^2)/2 + 1/4

    How is this possible?
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  2. #2
    MHF Contributor
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    The "error" is a side effect of doing the derivative badly, sorry.

    \frac{d}{dx}\left(\frac{x^{2}}{3}\right)\;=\;\frac  {2}{3}x\;\ne\;\frac{x}{6}

    Nice try, though. I am glad you are exploring rather than just doing the assigned problems. Keep asking questions.
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