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。
\[ \begin{equation}\begin{split}【1/1】求函数arccos(\frac{(a - sin(x)b)}{(cos(x)c)}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arccos(\frac{a}{ccos(x)} - \frac{bsin(x)}{ccos(x)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arccos(\frac{a}{ccos(x)} - \frac{bsin(x)}{ccos(x)})\right)}{dx}\\=&(\frac{-(\frac{asin(x)}{ccos^{2}(x)} - \frac{bcos(x)}{ccos(x)} - \frac{bsin(x)sin(x)}{ccos^{2}(x)})}{((1 - (\frac{a}{ccos(x)} - \frac{bsin(x)}{ccos(x)})^{2})^{\frac{1}{2}})})\\=&\frac{-asin(x)}{(\frac{-a^{2}}{c^{2}cos^{2}(x)} + \frac{2absin(x)}{c^{2}cos^{2}(x)} - \frac{b^{2}sin^{2}(x)}{c^{2}cos^{2}(x)} + 1)^{\frac{1}{2}}ccos^{2}(x)} + \frac{bsin^{2}(x)}{(\frac{-a^{2}}{c^{2}cos^{2}(x)} + \frac{2absin(x)}{c^{2}cos^{2}(x)} - \frac{b^{2}sin^{2}(x)}{c^{2}cos^{2}(x)} + 1)^{\frac{1}{2}}ccos^{2}(x)} + \frac{b}{(\frac{-a^{2}}{c^{2}cos^{2}(x)} + \frac{2absin(x)}{c^{2}cos^{2}(x)} - \frac{b^{2}sin^{2}(x)}{c^{2}cos^{2}(x)} + 1)^{\frac{1}{2}}c}\\ \end{split}\end{equation} \]

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