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

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