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

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