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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{(2(2x - 1)ln(2x - 1) - 6x + 6)}{((2x - 1){\frac{1}{(x - 1)}}^{3})} + \frac{2{\frac{1}{(x - 1)}}^{2}}{({(2x - 1)}^{2})} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{4xln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{2ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{6x}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{2}{(2x - 1)^{2}(x - 1)^{2}} + \frac{6}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{4xln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{2ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{6x}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{2}{(2x - 1)^{2}(x - 1)^{2}} + \frac{6}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})}\right)}{dx}\\=&4(\frac{-(2(\frac{-3(1 + 0)}{(x - 1)^{4}})x + \frac{2}{(x - 1)^{3}} - (\frac{-3(1 + 0)}{(x - 1)^{4}}))}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}})xln(2x - 1) + \frac{4ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{4x(2 + 0)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})(2x - 1)} - 2(\frac{-(2(\frac{-3(1 + 0)}{(x - 1)^{4}})x + \frac{2}{(x - 1)^{3}} - (\frac{-3(1 + 0)}{(x - 1)^{4}}))}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}})ln(2x - 1) - \frac{2(2 + 0)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})(2x - 1)} - 6(\frac{-(2(\frac{-3(1 + 0)}{(x - 1)^{4}})x + \frac{2}{(x - 1)^{3}} - (\frac{-3(1 + 0)}{(x - 1)^{4}}))}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}})x - \frac{6}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{2(\frac{-2(2 + 0)}{(2x - 1)^{3}})}{(x - 1)^{2}} + \frac{2(\frac{-2(1 + 0)}{(x - 1)^{3}})}{(2x - 1)^{2}} + 6(\frac{-(2(\frac{-3(1 + 0)}{(x - 1)^{4}})x + \frac{2}{(x - 1)^{3}} - (\frac{-3(1 + 0)}{(x - 1)^{4}}))}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}})\\=&\frac{24x^{2}ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} - \frac{8xln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{3}} - \frac{24xln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} + \frac{4ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{8x}{(2x - 1)(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} + \frac{4ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{3}} + \frac{6ln(2x - 1)}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} - \frac{36x^{2}}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} + \frac{12x}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{3}} + \frac{54x}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} - \frac{8}{(2x - 1)^{3}(x - 1)^{2}} - \frac{4}{(x - 1)^{3}(2x - 1)^{2}} - \frac{4}{(2x - 1)(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})} - \frac{18}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{4}} - \frac{12}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})^{2}(x - 1)^{3}} - \frac{6}{(\frac{2x}{(x - 1)^{3}} - \frac{1}{(x - 1)^{3}})}\\ \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!