本次共计算 1 个题目：每一题对 x 求 2 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{tan(x)}{ln(arcsin(x))} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{tan(x)}{ln(arcsin(x))}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{tan(x)}{ln(arcsin(x))}\right)}{dx}\\=&\frac{-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})tan(x)}{ln^{2}(arcsin(x))(arcsin(x))} + \frac{sec^{2}(x)(1)}{ln(arcsin(x))}\\=&\frac{-tan(x)}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin(x)} + \frac{sec^{2}(x)}{ln(arcsin(x))}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-tan(x)}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin(x)} + \frac{sec^{2}(x)}{ln(arcsin(x))}\right)}{dx}\\=&\frac{-(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})tan(x)}{ln^{2}(arcsin(x))arcsin(x)} - \frac{-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})tan(x)}{(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin(x)} - \frac{(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})tan(x)}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))} - \frac{sec^{2}(x)(1)}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin(x)} + \frac{-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})sec^{2}(x)}{ln^{2}(arcsin(x))(arcsin(x))} + \frac{2sec^{2}(x)tan(x)}{ln(arcsin(x))}\\=&\frac{-xtan(x)}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin(x)} + \frac{2tan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{2}(x)} + \frac{tan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} - \frac{sec^{2}(x)}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin(x)} - \frac{sec^{2}(x)}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin(x)} + \frac{2tan(x)sec^{2}(x)}{ln(arcsin(x))}\\ \end{split}\end{equation} \]

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