I am trying to solve and verify the below equation using Mathematica.
$\frac{\partial}{\partial b} \sum_{i=1}^n y_i \log\left[ \frac{\sum_{i=1}^n y_i}{1-\prod_{i=1}^n (1-b)^{Exp[x_i\beta]}} \right]$
I tried to solve this on paper and I was able to obtain the following solution:
$\sum_{i=1}^n \left( \frac{(1-b)^{Exp[x_i \beta]-1} Exp[x_i \beta] y_i \prod_{i=1}^n (1-b)^{Exp[x_i \beta]} \sum_{i=1}^n\frac{Exp[x_i\beta]}{1-b}}{1-\prod_{i=1}^n(1-b)^Exp[x_i\beta]} \right)$
I usually verify my equations using Mathematica by plugging in numbers. However, in this case, Mathematica is unable to solve the first equation. So, I appreciate if any of you can share any information on this.
Thank you in advance.