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Homework Help: D/dx( ln( x^2 + y^2 ) )

  1. Apr 19, 2010 #1
    1. The problem statement, all variables and given/known data

    Find y' if y = ln( x^2 + y^2 )

    2. Relevant equations

    d / dx ( lnx ) = 1 / x

    3. The attempt at a solution

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

    I couldnt find a way to isolate y' on its own
     
  2. jcsd
  3. Apr 19, 2010 #2

    rock.freak667

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    Homework Helper

    Cross multiply by x2+y2


    y'(x2+y2)=2x+2y*y'

    Should be easier to simplify now.
     
  4. Apr 20, 2010 #3
    When I cross multiply y' / (2x + 2y * y') = (x^2 + y^2)^-1 I get:

    y' = (x^2 + y^2)^-1(2x + 2y * y') but the y' s arent isolated :(
     
  5. Apr 20, 2010 #4
    [tex]y' (x^2+y^2) = 2x+2yy'[/tex]

    [tex]y'(x^2+y^2)-2yy'=2x[/tex]

    take y' a common factor and complete ..
     
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