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Relationship between partial derivatives

  1. Jan 27, 2008 #1
    Hello,
    Can anyone please tell me how to get the relationship between partial derivatives at a point, that is, dy/dx|x = - df/dx|y / df/dy|x ?
     
  2. jcsd
  3. Jan 27, 2008 #2

    epenguin

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    You maybe meant dy/dx|f = - df/dx|y / df/dy|x ?
     
    Last edited: Jan 27, 2008
  4. Jan 27, 2008 #3

    mathwonk

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    f(x,y) = c, implies df/dx dx + f/dy dy = 0, now solve for dy/dx.
     
  5. Jan 27, 2008 #4

    mathwonk

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    the geometry is that a curve x(t),y(t) moving in the level set where f= c, has velocity vector (dx/dt, dy/dt) which is perpendicular to the gradient vector of f: (df/dx, df/dy).
     
  6. Jan 28, 2008 #5
    Thanks mathwonk i was able to get it. I did not understand the explanation in the second the post particularly why t has been introduced etc.
     
  7. Jan 28, 2008 #6

    mathwonk

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    well saying df/dx dx/dt + df/dy dy/dt = 0, is a dot product statement involving grad f and the velocity vector of (x(t),y(t)).

    it is a little harder to make geometric sense out of the similar equation df/dx dx + df/dy dy = 0, in terms of differentials.
     
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