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Implicit Differentiation

  1. Jun 1, 2009 #1
    1. The problem statement, all variables and given/known data
    8x^2-10xy+3y^2=26


    2. The attempt at a solution

    (8)(2x)-(-10x)y'+(y)(-10)+(3)(2y)y'=0

    16x+10x(y')-10y+6y(y')=0

    y'(10x+6y)+16x-10y=0

    y'(10x+6y)=10y-16x

    y'=(10y-16x)/(10x+6y)

    y'=(5y-8x)/(5x+3y)

    I know I'm doing something wrong but I can't see it for myself. Can someome point me into the right direction?
     
  2. jcsd
  3. Jun 1, 2009 #2

    rock.freak667

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    Where'd you get that extra minus sign from when differentiating -10xy?
     
  4. Jun 1, 2009 #3
    I differentiated (-10xy)
     
  5. Jun 1, 2009 #4

    rock.freak667

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    That -ve sign should be a + sign.
     
  6. Jun 1, 2009 #5
    I'm still getting (5y-8x)/(3y-5x)
     
  7. Jun 1, 2009 #6

    rock.freak667

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    What answer are you supposed to get?
     
  8. Jun 1, 2009 #7
    (8x-5y)/(5x-3y)
     
  9. Jun 1, 2009 #8

    rock.freak667

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    Well multiply both the numerator and denominator by -1.
     
  10. Jun 1, 2009 #9
    Only thing that I see happened was that y' was moved to the right side of the equation therefore changing the signs. After I done it that way, I got the correct answer. Go figure!
     
  11. Jun 2, 2009 #10

    HallsofIvy

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    As rockfreak667 said before, you already had the correct answer:
    (5y-8x)/(3y-5x)= (8x-5y)/(5x-3y)
     
  12. Jun 2, 2009 #11
    I have another problem as well.

    x + (sqrtx)(sqrty) = 2y

    1 + (x^1/2)/(2y^1/2)y' + (y^1/2)/(2x^1/2) = 2y'

    My question is why I suppose to multiply both sides by (2x^1/2 * y^1/2) and not both of the denominators?
     
  13. Jun 2, 2009 #12

    rock.freak667

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    the common denominator of those the terms (not the 1 and not the 2y') is 2x1/2y1/2
     
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