## relation within Gauss-Newton method for minimization

If we study model fit on a nonlinear regression model

, ,

and in the Gauss-Newton method, the update on the parameter $\theta$ from step $t$ to $t+1$ is to minimize the ￼sum of squares

.

Can we prove that (why) (part 1) the update is given in the following form:

,

(part 2) where is a matrix whose -th row is , and is a column vector whose -th entry is .

How to derive those relations? Thanks in advance!