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。
\[ \begin{equation}\begin{split}【1/1】求函数2{x}^{3}{\frac{1}{(x - 1)}}^{3} - 6{x}^{2}{\frac{1}{(x - 1)}}^{2} + \frac{6x}{(x - 1)} - 2x{\frac{1}{(x - 1)}}^{3} + 2{\frac{1}{(x - 1)}}^{3} + 2{\frac{1}{(x - 1)}}^{2} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{2x^{3}}{(x - 1)^{3}} - \frac{6x^{2}}{(x - 1)^{2}} + \frac{6x}{(x - 1)} - \frac{2x}{(x - 1)^{3}} + \frac{2}{(x - 1)^{3}} + \frac{2}{(x - 1)^{2}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{2x^{3}}{(x - 1)^{3}} - \frac{6x^{2}}{(x - 1)^{2}} + \frac{6x}{(x - 1)} - \frac{2x}{(x - 1)^{3}} + \frac{2}{(x - 1)^{3}} + \frac{2}{(x - 1)^{2}}\right)}{dx}\\=&2(\frac{-3(1 + 0)}{(x - 1)^{4}})x^{3} + \frac{2*3x^{2}}{(x - 1)^{3}} - 6(\frac{-2(1 + 0)}{(x - 1)^{3}})x^{2} - \frac{6*2x}{(x - 1)^{2}} + 6(\frac{-(1 + 0)}{(x - 1)^{2}})x + \frac{6}{(x - 1)} - 2(\frac{-3(1 + 0)}{(x - 1)^{4}})x - \frac{2}{(x - 1)^{3}} + 2(\frac{-3(1 + 0)}{(x - 1)^{4}}) + 2(\frac{-2(1 + 0)}{(x - 1)^{3}})\\=&\frac{-6x^{3}}{(x - 1)^{4}} + \frac{18x^{2}}{(x - 1)^{3}} - \frac{18x}{(x - 1)^{2}} + \frac{6x}{(x - 1)^{4}} - \frac{6}{(x - 1)^{4}} - \frac{6}{(x - 1)^{3}} + \frac{6}{(x - 1)}\\ \end{split}\end{equation} \]

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！