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

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