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。
\[ \begin{equation}\begin{split}【1/1】求函数arcsin((\frac{1}{3})(13 - 12sin(arccos(\frac{5cos(x)}{sqrt(169 + 120sin(x))})))) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arcsin(-4sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{13}{3})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arcsin(-4sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{13}{3})\right)}{dx}\\=&(\frac{(-4cos(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)}))(\frac{-(\frac{5*-sin(x)}{sqrt(120sin(x) + 169)} + \frac{5cos(x)*-(120cos(x) + 0)*\frac{1}{2}}{(120sin(x) + 169)(120sin(x) + 169)^{\frac{1}{2}}})}{((1 - (\frac{5cos(x)}{sqrt(120sin(x) + 169)})^{2})^{\frac{1}{2}})}) + 0)}{((1 - (-4sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{13}{3})^{2})^{\frac{1}{2}})})\\=&\frac{-20sin(x)cos(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)}))}{(-16sin^{2}(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{104}{3}sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) - \frac{160}{9})^{\frac{1}{2}}(\frac{-25cos^{2}(x)}{sqrt(120sin(x) + 169)^{2}} + 1)^{\frac{1}{2}}sqrt(120sin(x) + 169)} - \frac{1200cos^{2}(x)cos(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)}))}{(-16sin^{2}(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{104}{3}sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) - \frac{160}{9})^{\frac{1}{2}}(\frac{-25cos^{2}(x)}{sqrt(120sin(x) + 169)^{2}} + 1)^{\frac{1}{2}}(120sin(x) + 169)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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