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

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