How to calculate Likelihood Function? Please Please do step by step, don't do shortcuts!!! thanks

Likelihood Function The log-likelihood turns products into sums: n M (yilog p(x;) + (1 -y:)log(1 -p(x;))) i=1 n p(xi) = log(1 - p(x;)) + yilog 1 - p (x i ) 1=1 n n = log(1 - p(x;)) + M Vi(x;b) i=1 i-1 n n 1 = I'M log 1 +e-xib yi (x;b) 1-1Likelihood Function a Derivative with respect to one component b n al n exib M M abj 1 + exib Vij + yixij i=1 But, no exact solution, So approximation * Derivative of log and sigmoid function 2 (ex) = ex dx d 1 dx 1te-x Ite-x (1. 1te-x)