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B Implicit Differentiation

  1. Jun 12, 2017 #1
    For implicit differentiation, is dy/dx of x2+y2 = 50 the same as y2 = 50 - x2 ?

    From what I can take it, it'd be a no since.
    For x2+y2 = 50,
    d/dx (x2+y2) = d/dx (50) --- will eventually be ---> dy/dx = -x/y

    y2 = 50 - x2
    y = sqrt(50 - x2)
    dy/dx = .5(-x2+50)-.5*(-2x)
  2. jcsd
  3. Jun 12, 2017 #2


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    Derivatives (dy/dx) are operators on functions, not on equations. Your post is meaningless.
  4. Jun 12, 2017 #3


    Staff: Mentor

    You don't "take dy/dx of" anything. dy/dx is the derivative of y with respect to x. The two equations above are equivalent, meaning that any (x, y) pair that satisifies one equation also satisfies the other equation.

    If you differentiate both sides of either equation with respect to x, you should be able to find dy/dx.
    There's no need to solve for y. Just differentiate y2 implicitly with respect to x.
  5. Jun 12, 2017 #4


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    Gold Member

    Sub -in the value of y in the first equation ( and cancel out the twos on the second one).
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