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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{{(\frac{(x - 1)(x - 2)(x - 4)}{(x - 3)})}^{1}}{2} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{\frac{1}{2}x^{3}}{(x - 3)} - \frac{\frac{7}{2}x^{2}}{(x - 3)} + \frac{7x}{(x - 3)} - \frac{4}{(x - 3)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{\frac{1}{2}x^{3}}{(x - 3)} - \frac{\frac{7}{2}x^{2}}{(x - 3)} + \frac{7x}{(x - 3)} - \frac{4}{(x - 3)}\right)}{dx}\\=&\frac{1}{2}(\frac{-(1 + 0)}{(x - 3)^{2}})x^{3} + \frac{\frac{1}{2}*3x^{2}}{(x - 3)} - \frac{7}{2}(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2} - \frac{\frac{7}{2}*2x}{(x - 3)} + 7(\frac{-(1 + 0)}{(x - 3)^{2}})x + \frac{7}{(x - 3)} - 4(\frac{-(1 + 0)}{(x - 3)^{2}})\\=&\frac{-x^{3}}{2(x - 3)^{2}} + \frac{3x^{2}}{2(x - 3)} + \frac{7x^{2}}{2(x - 3)^{2}} - \frac{7x}{(x - 3)} - \frac{7x}{(x - 3)^{2}} + \frac{4}{(x - 3)^{2}} + \frac{7}{(x - 3)}\\ \end{split}\end{equation} \]

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