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Differentiating an Implicit Function: a Circle

  1. Apr 29, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the expression for the slope on the lower half of the circle y^2 + x^2 = 25.

    2. Attempt at a solution.

    The text says you get 2x + 2y(dy/dx) = 0.

    I got this and then solved for dy/dx to get dy/dx = -2y - 2x.

    Then, I substituted for y the x value-expression for the lower region, y = - sqrt(25 - x^2)

    and I got dy/dx = -2x - 2(sqrt(25 - x^2)).

    Now the text gets the answer in another way:

    2x + 2y(dy/dx) = 0;

    then, 2x + 2(sqrt(25 - x^2))dy/dx = 0;

    then, dy/dx = -2x/2(sqrt(25 - x^2)) = -x/sqrt(25 - x^2).

    I see what they did. But what's wrong with the way I did it? Are the two answers equivalent in some way that I don't see, or how is mine wrong?

    Thanks.
     
  2. jcsd
  3. Apr 29, 2016 #2
    Do you notice something wrong here? :)
     
  4. Apr 29, 2016 #3
    Wow. OK. Yes, I see it. I'm going for a walk!

    Thank you very much!
     
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