Iteratively Reweighted Least Squares (IRLS) and Gauss-Newton

I am studying nonlinear regression optimization methods. I want to show that the Gauss-Newton method can be seen as an IRLS. We want to maximize $$ - \sum_{i = 1}^{n} (y_i - h(\mathbf{x}_i^T \mathbf{\beta}))^2 $$ Approximating $h(\mathbf{x}_i^T \mathbf{\beta})$ we have $$ - \sum_{i = 1}^{n} [y_i - h(\mathbf{x}_i^T \mathbf{\beta}^{(t)}) - h'(\mathbf{x}_i^T \mathbf{\beta}) \mathbf{x}_i^T (\mathbf{\beta} - \mathbf{\beta}^{(t)}) ]^2 $$ and here I don't know what to do. The books I have read do not show what to do when you have any function $h$ , or that explain the Gauss-Newton method in a direct way. I would appreciate any kind of help or suggestions. I am also looking for references on the subject in this regard.