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。
\[ \begin{equation}\begin{split}【1/1】求函数arccot(\frac{({(1 + {x}^{\frac{1}{2}})}^{2})}{(1 - x)}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arccot(\frac{x}{(-x + 1)} + \frac{2x^{\frac{1}{2}}}{(-x + 1)} + \frac{1}{(-x + 1)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arccot(\frac{x}{(-x + 1)} + \frac{2x^{\frac{1}{2}}}{(-x + 1)} + \frac{1}{(-x + 1)})\right)}{dx}\\=&(\frac{((\frac{-(-1 + 0)}{(-x + 1)^{2}})x + \frac{1}{(-x + 1)} + 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})x^{\frac{1}{2}} + \frac{2*\frac{1}{2}}{(-x + 1)x^{\frac{1}{2}}} + (\frac{-(-1 + 0)}{(-x + 1)^{2}}))}{(1 + (\frac{x}{(-x + 1)} + \frac{2x^{\frac{1}{2}}}{(-x + 1)} + \frac{1}{(-x + 1)})^{2})})\\=&\frac{x}{(-x + 1)^{2}(\frac{x^{2}}{(-x + 1)^{2}} + \frac{4x^{\frac{3}{2}}}{(-x + 1)^{2}} + \frac{6x}{(-x + 1)^{2}} + \frac{4x^{\frac{1}{2}}}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + 1)} + \frac{1}{(-x + 1)(\frac{x^{2}}{(-x + 1)^{2}} + \frac{4x^{\frac{3}{2}}}{(-x + 1)^{2}} + \frac{6x}{(-x + 1)^{2}} + \frac{4x^{\frac{1}{2}}}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + 1)} + \frac{2x^{\frac{1}{2}}}{(-x + 1)^{2}(\frac{x^{2}}{(-x + 1)^{2}} + \frac{4x^{\frac{3}{2}}}{(-x + 1)^{2}} + \frac{6x}{(-x + 1)^{2}} + \frac{4x^{\frac{1}{2}}}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + 1)} + \frac{1}{(-x + 1)(\frac{x^{2}}{(-x + 1)^{2}} + \frac{4x^{\frac{3}{2}}}{(-x + 1)^{2}} + \frac{6x}{(-x + 1)^{2}} + \frac{4x^{\frac{1}{2}}}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + 1)x^{\frac{1}{2}}} + \frac{1}{(-x + 1)^{2}(\frac{x^{2}}{(-x + 1)^{2}} + \frac{4x^{\frac{3}{2}}}{(-x + 1)^{2}} + \frac{6x}{(-x + 1)^{2}} + \frac{4x^{\frac{1}{2}}}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + 1)}\\ \end{split}\end{equation} \]

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