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

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