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Math Help - Logarithmic Differentiation...8x or 8

  1. #1
    Senior Member nycmath's Avatar
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    Logarithmic Differentiation...8x or 8

    I found this interesting question in my textbook. I am to solve this rational function via implicit differentiation. This question is from a section of the chapter titled LOGARITHMIC DIFFERENTIATION.

    Find y double prime.

    y = [x^2 * sqrt{3x-2}]/(x-1)^2

    After much work, I found y" to be the following monster:

    [(2/x)+3/(2(3x-2)-2/(x-1)]*y where y is the original rational function given.

    My Answer is:

    y" = (3x^2-15x+8)/2(x-1)^3*sqrt{3x-2}

    The book's answer is:

    y" = (3x^2-15x+8x)/2(x-1)^3*sqrt{3x-2}

    My question: Where did 8x come from in the numerator? Can this be a typo?
    I worked out the problem several times and my answer has not included 8x in the numerator.
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    Re: Logarithmic Differentiation...8x or 8

    i think there is a printing mistake in the text book if the answer in the text is correct then -15x + 8x can be added to -7x
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    Re: Logarithmic Differentiation...8x or 8

    The correct answer is ((3x^2-15x+8)x)/(2x(x-1)^3 sqrt(3x-2)) . do it once again and correctly substitute the value of y
    Last edited by binu01234; October 28th 2013 at 09:15 AM. Reason: spelling mistake
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    Re: Logarithmic Differentiation...8x or 8

    i think u had done mistake in substituting the value of y there is x^2 in y so one x gets cancelled while substituting and other remains there.
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    Senior Member nycmath's Avatar
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    Re: Logarithmic Differentiation...8x or 8

    Quote Originally Posted by binu01234 View Post
    The correct answer is ((3x^2-15x+8)x)/(2x(x-1)^3 sqrt(3x-2)) . do it once again and correctly substitute the value of y
    Yes, but notice the x on top and 2x in the bottom. This is reduced to my original answer which is:

    y' = (3x^2-15x+8)/2(x-1)^3*sqrt{3x-2}

    It feels good to know that I got the right answer alone. I am not taking calculus 1 in a formal, college class arena. I am learning on my own. Not too bad for someone who is not a math major. Thanks again for your input.
    Last edited by nycmath; October 28th 2013 at 03:20 PM.
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    Senior Member nycmath's Avatar
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    Re: Logarithmic Differentiation...8x or 8

    Quote Originally Posted by binu01234 View Post
    i think u had done mistake in substituting the value of y there is x^2 in y so one x gets cancelled while substituting and other remains there.
    No error at my end. It is a simple typo, which is typical in most math textbooks.
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  7. #7
    Senior Member nycmath's Avatar
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    Re: Logarithmic Differentiation...8x or 8

    Correction:

    The answer is solved for y prime not y double prime. This was my typo.

    Correct answer is:

    y' = (3x^2-15x+8)/2(x-1)^3*sqrt{3x-2}
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