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Derivative of a complex function wrt x_i

  1. Dec 27, 2011 #1
    Given a function
    [tex]
    \sum_{j=0}^m(b_{ij}-euclid(x_i, x_j))^2,
    [/tex]
    where euclid(x_i, x_j) denotes the Euclidean distance (1D or 2D) between x_i and x_j.
    I'm supposed to find the derivative with respect to x_i.
    The sum sign and the dimensionality are the problem for me.
    Any help on how to solve this is appreciated.
     
  2. jcsd
  3. Jan 5, 2012 #2

    lanedance

    User Avatar
    Homework Helper

    try writing out the sum to help

    [tex] \sum_{j=0}^m(b_{ij}-euclid(x_i, x_j))^2 = (b_{i1}-euclid(x_i, x_1))^2 + (b_{i2}-euclid(x_i, x_2))^2 +..+(b_{ii}-euclid(x_i, x_i))^2+..+(b_{im}-euclid(x_i, x_m))^2 [/tex]

    now differentiate term by term
     
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