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

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