There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{ln(sqrt(1 - sin(x)))}{sqrt(1 + sin(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{ln(sqrt(-sin(x) + 1))}{sqrt(sin(x) + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{ln(sqrt(-sin(x) + 1))}{sqrt(sin(x) + 1)}\right)}{dx}\\=&\frac{(-cos(x) + 0)*\frac{1}{2}}{(sqrt(-sin(x) + 1))(-sin(x) + 1)^{\frac{1}{2}}sqrt(sin(x) + 1)} + \frac{ln(sqrt(-sin(x) + 1))*-(cos(x) + 0)*\frac{1}{2}}{(sin(x) + 1)(sin(x) + 1)^{\frac{1}{2}}}\\=&\frac{-cos(x)}{2(-sin(x) + 1)^{\frac{1}{2}}sqrt(-sin(x) + 1)sqrt(sin(x) + 1)} - \frac{ln(sqrt(-sin(x) + 1))cos(x)}{2(sin(x) + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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