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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(sin(x + 120) - sin(x))}{(sin(x + 2400) - sin(x))} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{sin(x + 120)}{(sin(x + 2400) - sin(x))} - \frac{sin(x)}{(sin(x + 2400) - sin(x))}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{sin(x + 120)}{(sin(x + 2400) - sin(x))} - \frac{sin(x)}{(sin(x + 2400) - sin(x))}\right)}{dx}\\=&(\frac{-(cos(x + 2400)(1 + 0) - cos(x))}{(sin(x + 2400) - sin(x))^{2}})sin(x + 120) + \frac{cos(x + 120)(1 + 0)}{(sin(x + 2400) - sin(x))} - (\frac{-(cos(x + 2400)(1 + 0) - cos(x))}{(sin(x + 2400) - sin(x))^{2}})sin(x) - \frac{cos(x)}{(sin(x + 2400) - sin(x))}\\=&\frac{-sin(x + 120)cos(x + 2400)}{(sin(x + 2400) - sin(x))^{2}} + \frac{sin(x + 120)cos(x)}{(sin(x + 2400) - sin(x))^{2}} + \frac{cos(x + 120)}{(sin(x + 2400) - sin(x))} + \frac{sin(x)cos(x + 2400)}{(sin(x + 2400) - sin(x))^{2}} - \frac{sin(x)cos(x)}{(sin(x + 2400) - sin(x))^{2}} - \frac{cos(x)}{(sin(x + 2400) - sin(x))}\\ \end{split}\end{equation} \]

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