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Math Help - Implicit differentiation!

  1. #1
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    Implicit differentiation!

    Hi all
    I am trying to solve the following problem and my answer does not match up with that in the book.I have done it 4 times and have got it wrong each time.
    Can somebody do it before it drives me mad.

    Find dy/dx as a function of x and y for y=x-y+2y^3-3Lnx

    differentiate both sides;

    dy/dx= 1-(dy/dx)+6y^2.(dy/dx)-3x^-1

    2dy/dx-6y^2.(dy/dx)=1-3x^-1

    dy/dx(2-6y^2)=1-3x^-1

    dy/dx=(1-3x^-1)/ (2-6y^2)

    The answer in my book is dy/dx=(x-3)/[3x(1+2y^2)]

    I have followed the examples in the book fine, -this one is driving me mad.

    Help appreciated
    John
    Last edited by mr fantastic; August 19th 2011 at 03:06 PM. Reason: Deleted exess !'s in title.
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  2. #2
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    Re: Implicit differentiation!

    Quote Originally Posted by celtic1234 View Post
    Hi all
    I am trying to solve the following problem and my answer does not match up with that in the book.I have done it 4 times and have got it wrong each time.
    Can somebody do it before it drives me mad.

    Find dy/dx as a function of x and y for y=x-y+2y^3-3Lnx

    differentiate both sides;

    dy/dx= 1-(dy/dx)+6y^2.(dy/dx)-3x^-1

    2dy/dx-6y^2.(dy/dx)=1-3x^-1

    dy/dx(2-6y^2)=1-3x^-1

    dy/dx=(1-3x^-1)/ (2-6y^2)

    The answer in my book is dy/dx=(x-3)/[3x(1+2y^2)]

    I have followed the examples in the book fine, -this one is driving me mad.

    Help appreciated
    John
    I get \frac{dy}{dx} = \frac{x - 3}{2x(1 - 3y^2)}, which is consistent with your answer. So either the answer in the book is wrong or there is a typo in the original question.
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  3. #3
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    Re: Implicit differentiation!

    thank you,
    It is basic enough which was the reason it bothered me that i could not get it correct.
    Anyone else think it's a typo?
    thanks again
    John
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