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

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