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。\[ \begin{equation}\begin{split}【1/1】求函数x - \frac{(2({x}^{3}) - 25.91005({x}^{2}) + 12.87x - 1.469754)}{(6({x}^{2}) - 51.8201x + 12.87)} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x - \frac{2x^{3}}{(6x - 51.8201x + 12.87)} + \frac{25.91005x^{2}}{(6x - 51.8201x + 12.87)} - \frac{12.87x}{(6x - 51.8201x + 12.87)} + \frac{1.469754}{(6x - 51.8201x + 12.87)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( x - \frac{2x^{3}}{(6x - 51.8201x + 12.87)} + \frac{25.91005x^{2}}{(6x - 51.8201x + 12.87)} - \frac{12.87x}{(6x - 51.8201x + 12.87)} + \frac{1.469754}{(6x - 51.8201x + 12.87)}\right)}{dx}\\=&1 - 2(\frac{-(6 - 51.8201 + 0)}{(6x - 51.8201x + 12.87)^{2}})x^{3} - \frac{2*3x^{2}}{(6x - 51.8201x + 12.87)} + 25.91005(\frac{-(6 - 51.8201 + 0)}{(6x - 51.8201x + 12.87)^{2}})x^{2} + \frac{25.91005*2x}{(6x - 51.8201x + 12.87)} - 12.87(\frac{-(6 - 51.8201 + 0)}{(6x - 51.8201x + 12.87)^{2}})x - \frac{12.87}{(6x - 51.8201x + 12.87)} + 1.469754(\frac{-(6 - 51.8201 + 0)}{(6x - 51.8201x + 12.87)^{2}})\\=& - \frac{91.6402x^{3}}{(6x - 51.8201x + 12.87)(6x - 51.8201x + 12.87)} - \frac{6x^{2}}{(6x - 51.8201x + 12.87)} + \frac{1187.201082005x^{2}}{(6x - 51.8201x + 12.87)(6x - 51.8201x + 12.87)} + \frac{51.8201x}{(6x - 51.8201x + 12.87)} - \frac{589.704687x}{(6x - 51.8201x + 12.87)(6x - 51.8201x + 12.87)} + \frac{67.3442752554}{(6x - 51.8201x + 12.87)(6x - 51.8201x + 12.87)} - \frac{12.87}{(6x - 51.8201x + 12.87)} + 1\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!