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。
\[ \begin{equation}\begin{split}【1/1】求函数ln(\frac{(1 + sin(x))}{(1 - sin(x))}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = ln(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})\right)}{dx}\\=&\frac{((\frac{-(-cos(x) + 0)}{(-sin(x) + 1)^{2}})sin(x) + \frac{cos(x)}{(-sin(x) + 1)} + (\frac{-(-cos(x) + 0)}{(-sin(x) + 1)^{2}}))}{(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})}\\=&\frac{sin(x)cos(x)}{(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})(-sin(x) + 1)^{2}} + \frac{cos(x)}{(-sin(x) + 1)(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})} + \frac{cos(x)}{(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})(-sin(x) + 1)^{2}}\\ \end{split}\end{equation} \]

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