There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-(ln(1 - sin(x)) + ln(sin(x) + 1))}{2} + \frac{1}{(4(1 + sin(x)))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-1}{2}ln(-sin(x) + 1) - \frac{1}{2}ln(sin(x) + 1) + \frac{1}{(4sin(x) + 4)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-1}{2}ln(-sin(x) + 1) - \frac{1}{2}ln(sin(x) + 1) + \frac{1}{(4sin(x) + 4)}\right)}{dx}\\=&\frac{\frac{-1}{2}(-cos(x) + 0)}{(-sin(x) + 1)} - \frac{\frac{1}{2}(cos(x) + 0)}{(sin(x) + 1)} + (\frac{-(4cos(x) + 0)}{(4sin(x) + 4)^{2}})\\=&\frac{cos(x)}{2(-sin(x) + 1)} - \frac{cos(x)}{2(sin(x) + 1)} - \frac{4cos(x)}{(4sin(x) + 4)^{2}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！