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Math Help - Two Hard Derivitive Problems

  1. #1
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    Two Hard Derivitive Problems

    DUE IN 2 HOURS (at 12AM eastern)



    1. ln(sqrt(2x-8)/(9x+5))






    2. ln(6x-11)/x((x^2+1)^(1/3))
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lmao View Post
    1. ln(sqrt(2x-8)/(9x+5))
    let y = ln(sqrt(2x-8)/(9x+5))
    => y = ln(sqrt(2x - 8) - ln(9x + 5)
    => y = (1/2)ln(2x - 8) - ln(9x + 5) ...........now we will take the derivative

    => y' = (1/2)*[1/(2x - 8)]*2 - 1/(9x + 5) * 9
    => y' = 1/(2x - 8) - 9/(9x + 5)


    2. ln(6x-11)/x((x^2+1)^(1/3))
    let y = ln(6x-11)/x((x^2+1)^(1/3))
    by the quotient rule (and chain rule and product rule, we'll use them all)

    y' = {[x((x^2+1)^(1/3))]*6/(6x - 11) - ln(6x - 11)*[(x^2 + 1)^(1/3) + (x/3)(x^2 + 1)^(-2/3) * 2x]}/[x((x^2+1)^(1/3))]^2

    now we simplify this monstrosity

    y ' = {[6x((x^2+1)^(1/3))]/(6x - 11) - ln(6x - 11)(x^2 + 1)^(-2/3) * (x^2 + 1 + (2x^2)/3}/[x((x^2+1)^(1/3))]^2

    ...and so on...

    i'm really not in the mood to simplify this further, good luck with it
    Last edited by Jhevon; March 25th 2007 at 07:40 PM.
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  3. #3
    Junior Member frenzy's Avatar
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    Quote Originally Posted by Jhevon View Post
    ...

    i'm really not in the mood to simplify this further, good luck with it
    Hopefully lmao put the prentices in the correct place.

    For some reason I'm guessing not.

    Correct me
    lmao if I am wrong.
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  4. #4
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    I forgot to mention for the second one it says d(y)/d(x) then y="
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