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Implicit Derivation

  1. Mar 3, 2012 #1
    1. The problem statement, all variables and given/known data
    I am suppose to find the second derivative implicitly of the function y^2 = x^3. I find the first derivative to be dy/dx = 3x^2/2y, but shortly find myself having difficulty in the second derivation. My steps for the second derivative is in the file attached; there are a few additionally steps, but, at the last step, I am in no way nearing the actual answer.


    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Mar 3, 2012 #2

    SammyS

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    attachment.php?attachmentid=44684&d=1330827924.jpg

    I assume that you result for implicitly differentiating y^2 = x^3, the first time was something like:
    [itex]\displaystyle 2y(dy/dx)=3x^2[/itex]​
    Differentiate that again before solving for dy/dx. It's easier to work with.
     
  4. Mar 4, 2012 #3
    Well, I took the derivative from where you advised me to; but I still feel I am getting it wrong. Here are some of the steps I took, though there are few because I had the intuition that I was getting them wrong.
     

    Attached Files:

  5. Mar 4, 2012 #4

    SammyS

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    attachment.php?attachmentid=44708&d=1330867488.jpg

    That looks OK so far.
     
  6. Mar 4, 2012 #5
    Well, the answer is 3x/4y, and I am still not getting this.
     
  7. Mar 4, 2012 #6

    ehild

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    You miss a square in the second step . d/dx(yy')=y'2+yy".

    ehild
     
  8. Mar 4, 2012 #7
    ehild, I am terribly sorry: I don't really understand what you are saying; I can't not see what it is that I should be fixing in my second step.
     
  9. Mar 4, 2012 #8
    ehild, I believe you may have made a mistake when typing with latex.
     
  10. Mar 4, 2012 #9

    ehild

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    Do again the derivative of y dy/dx. It is (dy/dx)2+yd2y/dx2.

    ehild
     
  11. Mar 4, 2012 #10

    SammyS

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    I was wrong. As ehild pointed out, the dy/dx should be squared.

    [itex]\displaystyle \frac{d}{dx}(2y\frac{dy}{dx})=2\frac{dy}{dx}\frac{dy}{dx}+2y\frac{d^2y}{dx^2}[/itex]
     
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