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Implicit Differentiation Problem

  1. Oct 7, 2007 #1
    1. The problem statement, all variables and given/known datax[tex]^{}2[/tex](x-y)[tex]^{}2[/tex]=x[tex]^{}2[/tex]-y[tex]^{}2[/tex]

    2. Relevant equations

    3. The attempt at a solution

    I can get this far: x[2(x-y)(1-dy/dx)]+2x(x-y)=2x-2ydy/dx

    Any small hint as to where to go from here would be much appreciated.
  2. jcsd
  3. Oct 7, 2007 #2


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    What is the question?
    You posted an equation,
    [tex]x^2(x - y)^2 = x^2 - y^2[/tex]
    (and the way you posted it makes me wonder why you did just the superscript in LaTeX which didn't really make it a superscript anymore :smile:) and then went on to write a differential equation. :confused:
  4. Oct 7, 2007 #3


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    I assume, CompuChip, that the actual problem was in the title: "implicit differentiation problem". That is, to use implicit differentiation to find dy/dx when [itex]x^2(x-y)^2= x^2- y^2[/itex].

    Mathos, it's a real good idea to actually state the problem in the post!

    You say you have differentiated to get x[2(x-y)(1-dy/dx)]+2x(x-y)=2x-2ydy/dx (warning: I did not check that!) Now you want to solve that equation for dy/dx. Since differentiation is "linear", that is always a simple linear equation in dy/dx. Go ahead and multiply the left side to get -2x(x-y)dy/dx and add 2y dy/dx to both sides to isolate dy/dx. The divide by its coefficient.
    Last edited: Oct 17, 2007
  5. Oct 16, 2007 #4
    Your not supposed to give the answer right away. Your supposed to give clues to how to do it. Ever hear the phrase Give a man a fish; you feed him for a day. Teach a man to fish; you feed him for life.
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