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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{2ln(\frac{({x}^{\frac{1}{2}} + 1)}{(x - {x}^{\frac{1}{2}} + 1)})}{3} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{2}{3}ln(\frac{x^{\frac{1}{2}}}{(x - x^{\frac{1}{2}} + 1)} + \frac{1}{(x - x^{\frac{1}{2}} + 1)})\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{2}{3}ln(\frac{x^{\frac{1}{2}}}{(x - x^{\frac{1}{2}} + 1)} + \frac{1}{(x - x^{\frac{1}{2}} + 1)})\right)}{dx}\\=&\frac{\frac{2}{3}((\frac{-(1 - \frac{\frac{1}{2}}{x^{\frac{1}{2}}} + 0)}{(x - x^{\frac{1}{2}} + 1)^{2}})x^{\frac{1}{2}} + \frac{\frac{1}{2}}{(x - x^{\frac{1}{2}} + 1)x^{\frac{1}{2}}} + (\frac{-(1 - \frac{\frac{1}{2}}{x^{\frac{1}{2}}} + 0)}{(x - x^{\frac{1}{2}} + 1)^{2}}))}{(\frac{x^{\frac{1}{2}}}{(x - x^{\frac{1}{2}} + 1)} + \frac{1}{(x - x^{\frac{1}{2}} + 1)})}\\=&\frac{-2x^{\frac{1}{2}}}{3(x - x^{\frac{1}{2}} + 1)^{2}(\frac{x^{\frac{1}{2}}}{(x - x^{\frac{1}{2}} + 1)} + \frac{1}{(x - x^{\frac{1}{2}} + 1)})} + \frac{1}{3(x - x^{\frac{1}{2}} + 1)(\frac{x^{\frac{1}{2}}}{(x - x^{\frac{1}{2}} + 1)} + \frac{1}{(x - x^{\frac{1}{2}} + 1)})x^{\frac{1}{2}}} + \frac{1}{3(x - x^{\frac{1}{2}} + 1)^{2}(\frac{x^{\frac{1}{2}}}{(x - x^{\frac{1}{2}} + 1)} + \frac{1}{(x - x^{\frac{1}{2}} + 1)})x^{\frac{1}{2}}} - \frac{1}{3(x - x^{\frac{1}{2}} + 1)^{2}(\frac{x^{\frac{1}{2}}}{(x - x^{\frac{1}{2}} + 1)} + \frac{1}{(x - x^{\frac{1}{2}} + 1)})}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!