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。
\[ \begin{equation}\begin{split}【1/1】求函数{(\frac{(1 + sin(x))}{(1 - sin(x))})}^{\frac{1}{3}} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})^{\frac{1}{3}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( (\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})^{\frac{1}{3}}\right)}{dx}\\=&(\frac{\frac{1}{3}((\frac{-(-cos(x) + 0)}{(-sin(x) + 1)^{2}})sin(x) + \frac{cos(x)}{(-sin(x) + 1)} + (\frac{-(-cos(x) + 0)}{(-sin(x) + 1)^{2}}))}{(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})^{\frac{2}{3}}})\\=&\frac{sin(x)cos(x)}{3(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})^{\frac{2}{3}}(-sin(x) + 1)^{2}} + \frac{cos(x)}{3(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})^{\frac{2}{3}}(-sin(x) + 1)} + \frac{cos(x)}{3(\frac{sin(x)}{(-sin(x) + 1)} + \frac{1}{(-sin(x) + 1)})^{\frac{2}{3}}(-sin(x) + 1)^{2}}\\ \end{split}\end{equation} \]

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