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。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{3}{2})sin(2arctan(sqrt(\frac{(3 - 2x)}{(3 + 2x)}))) - 3arctan(sqrt(\frac{(3 - 2x)}{(3 + 2x)})) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{3}{2}sin(2arctan(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)}))) - 3arctan(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)}))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{3}{2}sin(2arctan(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)}))) - 3arctan(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)}))\right)}{dx}\\=&\frac{3}{2}cos(2arctan(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})))*2(\frac{(\frac{(-2(\frac{-(2 + 0)}{(2x + 3)^{2}})x - \frac{2}{(2x + 3)} + 3(\frac{-(2 + 0)}{(2x + 3)^{2}}))*\frac{1}{2}}{(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{\frac{1}{2}}})}{(1 + (sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)}))^{2})}) - 3(\frac{(\frac{(-2(\frac{-(2 + 0)}{(2x + 3)^{2}})x - \frac{2}{(2x + 3)} + 3(\frac{-(2 + 0)}{(2x + 3)^{2}}))*\frac{1}{2}}{(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{\frac{1}{2}}})}{(1 + (sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)}))^{2})})\\=&\frac{6xcos(2arctan(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})))}{(2x + 3)^{2}(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{\frac{1}{2}}(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{2} + 1)} - \frac{3cos(2arctan(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})))}{(2x + 3)(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{\frac{1}{2}}(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{2} + 1)} - \frac{9cos(2arctan(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})))}{(2x + 3)^{2}(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{\frac{1}{2}}(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{2} + 1)} - \frac{6x}{(2x + 3)^{2}(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{\frac{1}{2}}(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{2} + 1)} + \frac{9}{(2x + 3)^{2}(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{\frac{1}{2}}(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{2} + 1)} + \frac{3}{(2x + 3)(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{\frac{1}{2}}(sqrt(\frac{-2x}{(2x + 3)} + \frac{3}{(2x + 3)})^{2} + 1)}\\ \end{split}\end{equation} \]

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