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Math Help - Mult. choice implicit differentiation

  1. #1
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    Mult. choice implicit differentiation

    http://i43.tinypic.com/261dxqe.jpg

    I explained here^...this is just a practice quiz but I'm not sure if I have the right answer and they messed up the choices, OR if mine is just wrong.

    Thanks!
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  2. #2
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    I'm getting choice d.

    Convert it to xy^2 -xy + x - y = 0

    Take -(d/dx)/(d/dy)

    d/dx = y^2 - y + 1
    d/dy = 2xy - x - 1
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  3. #3
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    I'm not sure what you did but never mind I got it--I forgot to make something negative. D is right.

    Thanks anyway :]
    Last edited by janedoe; April 22nd 2009 at 01:33 PM.
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  4. #4
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    Ok, move the y to the other side of the equals sign so that you get this:

    xy^2 -xy + x - y = 0

    Now, implicitly derive (i'll group each piece)

    (y^2 + 2xyy') - (y + xy') + 1 - y' = 0

    Now you move y^2 - y + 1 to the other side of the equals sign

    2xyy' + xy' - y' = -(y^2 - y + 1)

    Now factor out y'

    y'(2xy + x - 1) = -(y^2 - y + 1)

    And finally divide by (2xy + x - 1)

    If you noticed, what you essentially did was move d/dx to the other side of the equals sign and divide d/dy.

    Hence -(d/dx)/(d/dy) being the shortcut to implicitely deriving.
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