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Math Help - Using Quotient Rule to find y'

  1. #1
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    Using Quotient Rule to find y'

    Hey guys!

    The following question asks me to find y' via the quotient rule.



    I know the quotient rule is:

    [f'(x)*g(x) - f(x)*g'(x)]/g(x)^2

    so i got:

    [3x^2+2]*[(4x^2-ln(x)^2] - [x^3-2x]*2[4x^2-ln(x)] divided by [4x^2-ln(x)]^4

    what i don't understand is, in the solution key, they throw (8x-1/x) in there.... where do they get that from?
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    MHF Contributor chisigma's Avatar
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    Is...

    \displaystyle \frac{d}{dx} (4\ x^{2} - \ln^{2} x)^{2} = 2\ (4\ x^{2} - \ln^{2} x)\ (8\ x -\frac{2}{x}\ \ln x)

    Kind regards

    \chi \sigma
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    thanks!
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