# Derivative of a complex function wrt x_i

1. Dec 27, 2011

### onako

Given a function
$$\sum_{j=0}^m(b_{ij}-euclid(x_i, x_j))^2,$$
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. Jan 5, 2012

### lanedance

try writing out the sum to help

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

now differentiate term by term