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。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{1}{2})ln({x}^{2} - 4x + 3) + (\frac{5}{4})ln(\frac{(x - 3)}{(x - 1)}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{1}{2}ln(x^{2} - 4x + 3) + \frac{5}{4}ln(\frac{x}{(x - 1)} - \frac{3}{(x - 1)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{1}{2}ln(x^{2} - 4x + 3) + \frac{5}{4}ln(\frac{x}{(x - 1)} - \frac{3}{(x - 1)})\right)}{dx}\\=&\frac{\frac{1}{2}(2x - 4 + 0)}{(x^{2} - 4x + 3)} + \frac{\frac{5}{4}((\frac{-(1 + 0)}{(x - 1)^{2}})x + \frac{1}{(x - 1)} - 3(\frac{-(1 + 0)}{(x - 1)^{2}}))}{(\frac{x}{(x - 1)} - \frac{3}{(x - 1)})}\\=&\frac{x}{(x^{2} - 4x + 3)} - \frac{5x}{4(x - 1)^{2}(\frac{x}{(x - 1)} - \frac{3}{(x - 1)})} + \frac{15}{4(x - 1)^{2}(\frac{x}{(x - 1)} - \frac{3}{(x - 1)})} + \frac{5}{4(\frac{x}{(x - 1)} - \frac{3}{(x - 1)})(x - 1)} - \frac{2}{(x^{2} - 4x + 3)}\\ \end{split}\end{equation} \]

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