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anonymous

  • 4 years ago

Use logarithmic differentiation to find the derivative of the function: (Wolfram|Alpha didn't work)

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  1. anonymous
    • 4 years ago
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  2. TuringTest
    • 4 years ago
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    what did you get after taking the natural log of both sides?

  3. anonymous
    • 4 years ago
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    Thats what I'm having trouble with

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  4. TuringTest
    • 4 years ago
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    you don't need to repost the problem I can still see it remember all you log rules, in particular these\[\log(\frac a b)=\log a-\log b\]\[\log(x^a)=a\log x\]then you will differentiate implicitly, which will allow you to solve for y'. why don't you try it and see how far you get?

  5. TuringTest
    • 4 years ago
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    rewriting this as\[y=(\frac{x^2+1}{x^2-1})^{1/6}\]should make it more clear

  6. anonymous
    • 4 years ago
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    So (x^2+1)-(x^2-1) = 2?

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  7. TuringTest
    • 4 years ago
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    not quite...\[y=(\frac{x^2+1}{x^2-1})^{1/6}\]\[\ln y=\ln(\frac{x^2+1}{x^2-1})^{1/6}=\frac1 6\ln(\frac{x^2+1}{x^2-1})=\frac1 6[\ln(x^2+1)-\ln(x^2-1)]\]now differentiate both sides implicitly.

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