本次共计算 1 个题目：每一题对 x 求 3 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(x + 3)(x - 2)}{(x - 3)} 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{2}}{(x - 3)} + \frac{x}{(x - 3)} - \frac{6}{(x - 3)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x^{2}}{(x - 3)} + \frac{x}{(x - 3)} - \frac{6}{(x - 3)}\right)}{dx}\\=&(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2} + \frac{2x}{(x - 3)} + (\frac{-(1 + 0)}{(x - 3)^{2}})x + \frac{1}{(x - 3)} - 6(\frac{-(1 + 0)}{(x - 3)^{2}})\\=&\frac{-x^{2}}{(x - 3)^{2}} + \frac{2x}{(x - 3)} - \frac{x}{(x - 3)^{2}} + \frac{6}{(x - 3)^{2}} + \frac{1}{(x - 3)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-x^{2}}{(x - 3)^{2}} + \frac{2x}{(x - 3)} - \frac{x}{(x - 3)^{2}} + \frac{6}{(x - 3)^{2}} + \frac{1}{(x - 3)}\right)}{dx}\\=&-(\frac{-2(1 + 0)}{(x - 3)^{3}})x^{2} - \frac{2x}{(x - 3)^{2}} + 2(\frac{-(1 + 0)}{(x - 3)^{2}})x + \frac{2}{(x - 3)} - (\frac{-2(1 + 0)}{(x - 3)^{3}})x - \frac{1}{(x - 3)^{2}} + 6(\frac{-2(1 + 0)}{(x - 3)^{3}}) + (\frac{-(1 + 0)}{(x - 3)^{2}})\\=&\frac{2x^{2}}{(x - 3)^{3}} - \frac{4x}{(x - 3)^{2}} + \frac{2x}{(x - 3)^{3}} - \frac{12}{(x - 3)^{3}} - \frac{2}{(x - 3)^{2}} + \frac{2}{(x - 3)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2x^{2}}{(x - 3)^{3}} - \frac{4x}{(x - 3)^{2}} + \frac{2x}{(x - 3)^{3}} - \frac{12}{(x - 3)^{3}} - \frac{2}{(x - 3)^{2}} + \frac{2}{(x - 3)}\right)}{dx}\\=&2(\frac{-3(1 + 0)}{(x - 3)^{4}})x^{2} + \frac{2*2x}{(x - 3)^{3}} - 4(\frac{-2(1 + 0)}{(x - 3)^{3}})x - \frac{4}{(x - 3)^{2}} + 2(\frac{-3(1 + 0)}{(x - 3)^{4}})x + \frac{2}{(x - 3)^{3}} - 12(\frac{-3(1 + 0)}{(x - 3)^{4}}) - 2(\frac{-2(1 + 0)}{(x - 3)^{3}}) + 2(\frac{-(1 + 0)}{(x - 3)^{2}})\\=&\frac{-6x^{2}}{(x - 3)^{4}} + \frac{12x}{(x - 3)^{3}} - \frac{6x}{(x - 3)^{4}} + \frac{36}{(x - 3)^{4}} + \frac{6}{(x - 3)^{3}} - \frac{6}{(x - 3)^{2}}\\ \end{split}\end{equation} \]

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