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anonymous

  • one year ago

differentiate y=(Inx)^squart root x Do not simplify answer

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  1. anonymous
    • one year ago
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    \[y=(\ln x)^{\sqrt{x}}\]

  2. zepdrix
    • one year ago
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    Hey Jess :) We can uhhh.. use logs I suppose, that should help

  3. zepdrix
    • one year ago
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    So umm.. ya ya let's try that. Let's take the natural log of each side.\[\large\rm \ln y= \ln\left[(\ln x)^{\sqrt x}\right]\]

  4. zepdrix
    • one year ago
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    Now we can apply our log rule to rewrite the right side,\[\large\rm \ln y=\sqrt{x} ~\ln\left[(\ln x)\right]\]And from there you'll apply product rule :) It's gonna get messy! Confused by any of that? :o

  5. anonymous
    • one year ago
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    im somewhat getting it

  6. zepdrix
    • one year ago
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    So let's first `set up` our derivative so we understand how it's going to look.\[\large\rm \color{royalblue}{(\ln y)'}=\color{royalblue}{(\sqrt x)'}\ln(\ln x)+\sqrt x\color{royalblue}{\left[\ln(\ln x)\right]'}\]The blue stuff is what we need to differentiate.

  7. zepdrix
    • one year ago
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    Product rule on the right, ya?

  8. zepdrix
    • one year ago
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    Too much? :O Brain esplode?

  9. anonymous
    • one year ago
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    no im still here

  10. zepdrix
    • one year ago
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    So then uhhh take some derivatives :) remember derivative of \(\large\rm \sqrt{x}\) ?

  11. nincompoop
    • one year ago
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    http://openstudy.com/study#/updates/559c9c4ae4b0564dd2d41b6a

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