thanks limitless problem

In logistic regression, you are working with a model that predicts probabilities of outcomes based on a set of features. The model's performance is measured using a score called the negative log-ikelihood (NLL), which penalizes predictions that deviate from the actual outcomes.

Given this negative log-ikelihood as a function of the model's weights, what is the derivative of the NLL with respect to the weights? Explain why this derivative matters in the context of improving the model's predictions and how the predicted probabilities and actual outcomes influence this gradient.