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Implicit derivative of function, calc 3

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data


    Find dy/dx ;

    sqrt(xy) = 1 + yx^2
    or
    0 = 1 + yx^2 - sqrt(xy)

    Definition :

    dy/dx = - F_x / F_y;

    A = F_x = 2xy - 1/2 (xy)^-0.5 * y
    B = F_y = x^2 - 1/2(xy)^-0.5 * x

    Then dy/dx = -A / B

    But the answer according to the book, is this :

    4(xy)^-1.5 - y
    --------------
    x - 2x^2/(sqrt(xy))
     
  2. jcsd
  3. Oct 12, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    They just multiplied numerator and denominator by 2*sqrt(xy).
     
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