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Homework Help: Implicit differentiation help

  1. Jul 2, 2010 #1
    can someone show me step by step how to find dy/dx of y=1/(x+y) using implicit differentiation?
     
  2. jcsd
  3. Jul 2, 2010 #2

    hunt_mat

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    if [tex]y=1/[x+y)[/tex] then [tex]y^{2}+xy=1[/tex]. Differentiate to obtain:
    [tex]
    2y\frac{dy}{dx}+y+x\frac{dy}{dx}=0
    [/tex]
    Re-arrange to obtain dy/dx
     
  4. Jul 2, 2010 #3

    hunt_mat

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    Or failing that [tex]y^{2}+xy-1=0[/tex] in a quadratic in y, solve this equation and you should have y=y(x) which is easy to differentiate!
     
  5. Jul 3, 2010 #4
    hunt_mat is correct. Rearranging is much quicker, but taking the quadratic route is very useful to check your answer.

    Edit: If I let v = x + y, then y = 1/v and dy/dx = -1/v^2 dv/dx. However, continuing this does not give me the right answer; why not? EDIT: Nevermind, I figured it out. :)
     
    Last edited: Jul 3, 2010
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