本次共计算 1 个题目：每一题对 x 求 4 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数tan(x) - arcsin(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( tan(x) - arcsin(x)\right)}{dx}\\=&sec^{2}(x)(1) - (\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})\\=&sec^{2}(x) - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( sec^{2}(x) - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&2sec^{2}(x)tan(x) - (\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})\\=&2tan(x)sec^{2}(x) - \frac{x}{(-x^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2tan(x)sec^{2}(x) - \frac{x}{(-x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&2sec^{2}(x)(1)sec^{2}(x) + 2tan(x)*2sec^{2}(x)tan(x) - (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x - \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}}\\=&2sec^{4}(x) + 4tan^{2}(x)sec^{2}(x) - \frac{3x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 2sec^{4}(x) + 4tan^{2}(x)sec^{2}(x) - \frac{3x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&2*4sec^{4}(x)tan(x) + 4*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 4tan^{2}(x)*2sec^{2}(x)tan(x) - 3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2} - \frac{3*2x}{(-x^{2} + 1)^{\frac{5}{2}}} - (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})\\=&16tan(x)sec^{4}(x) + 8tan^{3}(x)sec^{2}(x) - \frac{15x^{3}}{(-x^{2} + 1)^{\frac{7}{2}}} - \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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