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

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