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。
\[ \begin{equation}\begin{split}【1/1】求函数arctan(\frac{(\frac{18}{5}sin(\frac{6}{5}x) + 5)}{(3 - 3cos(\frac{6}{5})x + 5sqrt(35))}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arctan(\frac{\frac{18}{5}sin(\frac{6}{5}x)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)} + \frac{5}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arctan(\frac{\frac{18}{5}sin(\frac{6}{5}x)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)} + \frac{5}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)})\right)}{dx}\\=&(\frac{(\frac{18}{5}(\frac{-(-3cos(\frac{6}{5}) - 3x*-sin(\frac{6}{5})*0 + 5*0*\frac{1}{2}*35^{\frac{1}{2}} + 0)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}})sin(\frac{6}{5}x) + \frac{\frac{18}{5}cos(\frac{6}{5}x)*\frac{6}{5}}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)} + 5(\frac{-(-3cos(\frac{6}{5}) - 3x*-sin(\frac{6}{5})*0 + 5*0*\frac{1}{2}*35^{\frac{1}{2}} + 0)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}}))}{(1 + (\frac{\frac{18}{5}sin(\frac{6}{5}x)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)} + \frac{5}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)})^{2})})\\=&\frac{54sin(\frac{6}{5}x)cos(\frac{6}{5})}{5(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}(\frac{\frac{324}{25}sin^{2}(\frac{6}{5}x)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}} + \frac{36sin(\frac{6}{5}x)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}} + \frac{25}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}} + 1)} + \frac{108cos(\frac{6}{5}x)}{25(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)(\frac{\frac{324}{25}sin^{2}(\frac{6}{5}x)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}} + \frac{36sin(\frac{6}{5}x)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}} + \frac{25}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}} + 1)} + \frac{15cos(\frac{6}{5})}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}(\frac{\frac{324}{25}sin^{2}(\frac{6}{5}x)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}} + \frac{36sin(\frac{6}{5}x)}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}} + \frac{25}{(-3xcos(\frac{6}{5}) + 5sqrt(35) + 3)^{2}} + 1)}\\ \end{split}\end{equation} \]

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