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

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