I am working with the probability likelihood function $$ \log \prod\limits_{i=1}^{n} x_i^{y_i} + \log \prod\limits_{i=1}^{n}\left(1-{{x}_{i}}\right)^{n_i-y_i}. $$
I want to take the derivative with respect to $x_i$.
How should I do it? Thanks in advance.