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。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{1}{4}){x}^{3}{\frac{1}{(1 - {x}^{2})}}^{2} - \frac{(\frac{5}{8})x}{(1 - {x}^{2})} - (\frac{3}{8})ln(\frac{(1 + x)}{sqrt(1 - {x}^{2})}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{\frac{1}{4}x^{3}}{(-x^{2} + 1)^{2}} - \frac{\frac{5}{8}x}{(-x^{2} + 1)} - \frac{3}{8}ln(\frac{1}{sqrt(-x^{2} + 1)} + \frac{x}{sqrt(-x^{2} + 1)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{\frac{1}{4}x^{3}}{(-x^{2} + 1)^{2}} - \frac{\frac{5}{8}x}{(-x^{2} + 1)} - \frac{3}{8}ln(\frac{1}{sqrt(-x^{2} + 1)} + \frac{x}{sqrt(-x^{2} + 1)})\right)}{dx}\\=&\frac{1}{4}(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x^{3} + \frac{\frac{1}{4}*3x^{2}}{(-x^{2} + 1)^{2}} - \frac{5}{8}(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})x - \frac{\frac{5}{8}}{(-x^{2} + 1)} - \frac{\frac{3}{8}(\frac{-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{1}{sqrt(-x^{2} + 1)} + \frac{x*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}})}{(\frac{1}{sqrt(-x^{2} + 1)} + \frac{x}{sqrt(-x^{2} + 1)})}\\=&\frac{x^{4}}{(-x^{2} + 1)^{3}} - \frac{x^{2}}{2(-x^{2} + 1)^{2}} - \frac{3x^{2}}{8(-x^{2} + 1)^{\frac{3}{2}}(\frac{1}{sqrt(-x^{2} + 1)} + \frac{x}{sqrt(-x^{2} + 1)})} - \frac{3}{8(\frac{1}{sqrt(-x^{2} + 1)} + \frac{x}{sqrt(-x^{2} + 1)})sqrt(-x^{2} + 1)} - \frac{3x}{8(-x^{2} + 1)^{\frac{3}{2}}(\frac{1}{sqrt(-x^{2} + 1)} + \frac{x}{sqrt(-x^{2} + 1)})} - \frac{5}{8(-x^{2} + 1)}\\ \end{split}\end{equation} \]

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