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Very very short question on second derivative

  1. Oct 18, 2014 #1
    What does it mean when I have to find the second derivative of a circle at a given point? (Implicit diffing)

    In specifics, the equation is 9x2 +y2 =9
    At the point (0,3)
    You don't really need the rest at all, but it was just my process.

    This seems to make no sense.
    first D'v 18x+2yy'=0
    Second derivative gives 18+y''=0
    Doesn't it?
    How am I supposed to substitute coordinates?
    Last edited: Oct 18, 2014
  2. jcsd
  3. Oct 18, 2014 #2


    Staff: Mentor

    That equation is not the first derivative. You need to solve for y' algebraically.
    No. When you have isolated y', differentiate it to get y''. Then, to find the value of y'' at (0, 3), substitute these coordinates in your formula.
  4. Oct 18, 2014 #3


    User Avatar
    Science Advisor

    Strictly speaking, it doesn't mean anything! You do not take the derivative of geometric objects, you take the derivative of functions. What you are asking about the relation describing the circle.
    That's not a circle, it's an ellipse.
    Using "implicit differentiation" as you say, you get 18x+ 2yy'= 0 where y' is the derivative with respect to x.
    Doing that again you do NOT get 18+ y''= 0. You forgot to use the product rule on 2yy'. Implicit differentiation gives, rather,
    Last edited by a moderator: Oct 19, 2014
  5. Oct 19, 2014 #4
    Okay, so if I differentiate once implicitly, I get 18+2yy'
    Then, algebra, so that it's -9/y = y'
    But if I differentiate that, then I have y prime and y double prime....
    Oh, so I can find y prime from the earlier equation, then resubsitute?

  6. Oct 19, 2014 #5


    Staff: Mentor

    That's the idea.
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