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。\[ \begin{equation}\begin{split}【1/1】求函数2{x}^{3} + 6x + 3ln(\frac{(x - 1)}{(x + 1)}) 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 2x^{3} + 6x + 3ln(\frac{x}{(x + 1)} - \frac{1}{(x + 1)})\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( 2x^{3} + 6x + 3ln(\frac{x}{(x + 1)} - \frac{1}{(x + 1)})\right)}{dx}\\=&2*3x^{2} + 6 + \frac{3((\frac{-(1 + 0)}{(x + 1)^{2}})x + \frac{1}{(x + 1)} - (\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{x}{(x + 1)} - \frac{1}{(x + 1)})}\\=&6x^{2} - \frac{3x}{(x + 1)^{2}(\frac{x}{(x + 1)} - \frac{1}{(x + 1)})} + \frac{3}{(x + 1)^{2}(\frac{x}{(x + 1)} - \frac{1}{(x + 1)})} + \frac{3}{(\frac{x}{(x + 1)} - \frac{1}{(x + 1)})(x + 1)} + 6\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!