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Implicit differentiation

  1. Sep 28, 2012 #1
    1. y = sinxy



    2. Relevant equations



    3. this was my attempt

    d/dx = (cosxy)(sinxy(d\dx))+(xy(d/dx)




    im getting stuck. i dont think im starting it right. any suggestions.
     
    Last edited by a moderator: Sep 28, 2012
  2. jcsd
  3. Sep 28, 2012 #2
    Some notes:

    Remember that you're solving for dy/dx. Look for terms that will contain this.

    Remember the chain rule for explicit differentiation: d/dx f(g(x)) = g'(x)*f'(g(x)). How do you apply the chain rule when you have f(g(x, y(x)))?
     
  4. Sep 29, 2012 #3

    is it like this?

    y(d/dx) = cosxy(cosxy(d/dx))(x(d/dx))(y(1))
     
  5. Sep 29, 2012 #4
    Sorry, I'm not really following your steps. Can you maybe show me step-by-step what you're doing?
     
  6. Sep 29, 2012 #5
    use sin^-1 (y)=xy and then differentiate both sides
     
  7. Sep 29, 2012 #6
    im trying to do this f(g(x, y(x)))

    for the left side
     
  8. Sep 29, 2012 #7
    Your overall goal is to find dy/dx, right? So you need to apply d/dx to both sides of the equation -- d/dx (y) = d/dx (sin(xy)). The left side is simply y, so you don't need to apply the chain rule -- just take d/dx (y) = dy/dx. The right side requires the chain rule. This is where your composite function is.
     
  9. Sep 29, 2012 #8

    HallsofIvy

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    Science Advisor

    Don't write "d/dx". You mean "dy/dx" or d(xy)/dx.
    When you wrote "d/dx = (cosxy)(sinxy(d\dx))+(xy(d/dx)", you meant
    dy/dx= cos(xy)(d(xy)/dx)= cos(xy)((dx/dx)y+ x(dy/dx))
     
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