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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{45sqrt(arccos(1 - \frac{2x}{90}) - \frac{sin(2arccos(1 - \frac{2x}{90}))}{2})}{sqrt(pi)} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{45sqrt(arccos(\frac{-1}{45}x + 1) - \frac{1}{2}sin(2arccos(\frac{-1}{45}x + 1)))}{sqrt(pi)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{45sqrt(arccos(\frac{-1}{45}x + 1) - \frac{1}{2}sin(2arccos(\frac{-1}{45}x + 1)))}{sqrt(pi)}\right)}{dx}\\=&\frac{45*-0*\frac{1}{2}sqrt(arccos(\frac{-1}{45}x + 1) - \frac{1}{2}sin(2arccos(\frac{-1}{45}x + 1)))}{(pi)(pi)^{\frac{1}{2}}} + \frac{45((\frac{-(\frac{-1}{45} + 0)}{((1 - (\frac{-1}{45}x + 1)^{2})^{\frac{1}{2}})}) - \frac{1}{2}cos(2arccos(\frac{-1}{45}x + 1))*2(\frac{-(\frac{-1}{45} + 0)}{((1 - (\frac{-1}{45}x + 1)^{2})^{\frac{1}{2}})}))*\frac{1}{2}}{sqrt(pi)(arccos(\frac{-1}{45}x + 1) - \frac{1}{2}sin(2arccos(\frac{-1}{45}x + 1)))^{\frac{1}{2}}}\\=&\frac{1}{2(\frac{-1}{2025}x^{2} + \frac{2}{45}x)^{\frac{1}{2}}(arccos(\frac{-1}{45}x + 1) - \frac{1}{2}sin(2arccos(\frac{-1}{45}x + 1)))^{\frac{1}{2}}sqrt(pi)} - \frac{cos(2arccos(\frac{-1}{45}x + 1))}{2(\frac{-1}{2025}x^{2} + \frac{2}{45}x)^{\frac{1}{2}}(arccos(\frac{-1}{45}x + 1) - \frac{1}{2}sin(2arccos(\frac{-1}{45}x + 1)))^{\frac{1}{2}}sqrt(pi)}\\ \end{split}\end{equation} \]

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