Find derivative of a complicated fraction

Question

Let $n> 1$ be an integer and let $x_1,\ldots,x_n$ be positive real numbers, all between $0$ and $1$. Is it possible to find the derivative of it so I know if it is increasing wrt $x_i$? $$ \frac{\sum_{i=1}^{n}x_i}{1-\prod_{i=1}^{n}(1-x_i)}\ $$ I thought about expanding it to $$ \frac{x_1+x_2+...x_i}{1-(1-x_1)(1-x_2)...(1-x_i)}\ $$

Answer 1

Hint: Let $$A=\sum_{j\neq i}x_j$$ $$B=\prod_{j\neq i}(1-x_j)$$