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。
\[ \begin{equation}\begin{split}【1/1】求函数xsqrt(\frac{(x - 1)(x - 2)}{((x - 3)(x - 4))}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = xsqrt(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( xsqrt(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})\right)}{dx}\\=&sqrt(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)}) + \frac{x((\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2} + \frac{2x}{(x^{2} - 7x + 12)} - 3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x - \frac{3}{(x^{2} - 7x + 12)} + 2(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}}))*\frac{1}{2}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}}\\=&sqrt(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)}) - \frac{x^{4}}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{13x^{3}}{2(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{x^{2}}{(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{25x^{2}}{2(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{3x}{2(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{7x}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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