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Implicit Differentiation Help

  1. Jul 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Find dy / dx for sqrt(xy) = x - 2y.


    2. Relevant equations

    I don't know how to simplify

    [(xy' + y) / 2sqrt(xy)] = (1 - 2y')

    to

    y' = [- y + 2sqrt(xy)] / [x + 4sqrt(xy)].


    3. The attempt at a solution

    I do everything Wolfram Alpha does here:

    http://www.wolframalpha.com/input/?i=derivative+sqrt(xy)+=+x+-+2y

    and at the end of the steps shown above, I want to multiply (1 - 2y') by 2sqrt(xy), to get

    2sqrt(xy) - 4y'sqrt(xy)

    although I don't think that's correct.

    Help please.

    I just realized all I d is solve for y' (didn't occur to me for some reason), and now need to know if I plug in the original equation into all of the y values (I think I remember seeing my prof. do this in class). Ayuda me por favor.
     
    Last edited by a moderator: Jul 12, 2012
  2. jcsd
  3. Jul 11, 2012 #2

    eumyang

    User Avatar
    Homework Helper

    Yes, that's correct. Now rearrange the terms so that the ones with y' are on one side, and the other terms are on the other. Solve for y'.


    EDIT: It looks like you figured it out already.
     
  4. Jul 12, 2012 #3
    Thanks. I appreciate it.
     
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