本次共计算 1 个题目：每一题对 x 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{-1}{2})ln(\frac{(1 + cos(x))}{(1 - cos(x))}) + C 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{-1}{2}ln(\frac{cos(x)}{(-cos(x) + 1)} + \frac{1}{(-cos(x) + 1)}) + C\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{-1}{2}ln(\frac{cos(x)}{(-cos(x) + 1)} + \frac{1}{(-cos(x) + 1)}) + C\right)}{dx}\\=&\frac{\frac{-1}{2}((\frac{-(--sin(x) + 0)}{(-cos(x) + 1)^{2}})cos(x) + \frac{-sin(x)}{(-cos(x) + 1)} + (\frac{-(--sin(x) + 0)}{(-cos(x) + 1)^{2}}))}{(\frac{cos(x)}{(-cos(x) + 1)} + \frac{1}{(-cos(x) + 1)})} + 0\\=&\frac{sin(x)cos(x)}{2(-cos(x) + 1)^{2}(\frac{cos(x)}{(-cos(x) + 1)} + \frac{1}{(-cos(x) + 1)})} + \frac{sin(x)}{2(\frac{cos(x)}{(-cos(x) + 1)} + \frac{1}{(-cos(x) + 1)})(-cos(x) + 1)} + \frac{sin(x)}{2(-cos(x) + 1)^{2}(\frac{cos(x)}{(-cos(x) + 1)} + \frac{1}{(-cos(x) + 1)})}\\ \end{split}\end{equation} \]

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