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Derivatives - Product Rule

  1. Feb 3, 2014 #1
    Find y'
    y=(x2+1)7(x9+2)5(x3+1)3(x8+7)3

    Is there a shortcut to doing this problem? Or do I have to actually use the product rule more than 3 times?
     
  2. jcsd
  3. Feb 3, 2014 #2

    rock.freak667

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    Homework Helper

    The easiest way would be to just use the product rule. Using the chain rule might make it a bit easier in terms of making sure that you don't make a mistake.
     
  4. Feb 3, 2014 #3

    statdad

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    Homework Helper

    You could take logs of each side:
    [tex]
    \begin{align*}
    \ln y & = \ln{\left(x^2+1\right)^7 \left(x^9+2\right)^5 \left(x^3+1\right)^3 \left(x^8 + 7\right)^3} \\
    & = 7\ln(x^2+1) + 5\ln(x^9+1) + 3\ln(x^3+1) + 3\ln(x^8+7)
    \end{align*}
    [/tex]

    Differentiating gives
    [tex]
    \frac{y'}{y}
    [/tex]

    on the left and a sum of terms on the right: multiply through by [itex] y [/itex] and cancelling terms may make the work slightly more palatable.
     
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