本次共计算 1 个题目:每一题对 x 求 3 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数\frac{(-84{x}^{2} - 98x + 61)}{(-65x - 69)} 关于 x 的 3 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{-84x^{2}}{(-65x - 69)} - \frac{98x}{(-65x - 69)} + \frac{61}{(-65x - 69)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{-84x^{2}}{(-65x - 69)} - \frac{98x}{(-65x - 69)} + \frac{61}{(-65x - 69)}\right)}{dx}\\=&-84(\frac{-(-65 + 0)}{(-65x - 69)^{2}})x^{2} - \frac{84*2x}{(-65x - 69)} - 98(\frac{-(-65 + 0)}{(-65x - 69)^{2}})x - \frac{98}{(-65x - 69)} + 61(\frac{-(-65 + 0)}{(-65x - 69)^{2}})\\=&\frac{-5460x^{2}}{(-65x - 69)^{2}} - \frac{168x}{(-65x - 69)} - \frac{6370x}{(-65x - 69)^{2}} + \frac{3965}{(-65x - 69)^{2}} - \frac{98}{(-65x - 69)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{-5460x^{2}}{(-65x - 69)^{2}} - \frac{168x}{(-65x - 69)} - \frac{6370x}{(-65x - 69)^{2}} + \frac{3965}{(-65x - 69)^{2}} - \frac{98}{(-65x - 69)}\right)}{dx}\\=&-5460(\frac{-2(-65 + 0)}{(-65x - 69)^{3}})x^{2} - \frac{5460*2x}{(-65x - 69)^{2}} - 168(\frac{-(-65 + 0)}{(-65x - 69)^{2}})x - \frac{168}{(-65x - 69)} - 6370(\frac{-2(-65 + 0)}{(-65x - 69)^{3}})x - \frac{6370}{(-65x - 69)^{2}} + 3965(\frac{-2(-65 + 0)}{(-65x - 69)^{3}}) - 98(\frac{-(-65 + 0)}{(-65x - 69)^{2}})\\=&\frac{-709800x^{2}}{(-65x - 69)^{3}} - \frac{21840x}{(-65x - 69)^{2}} - \frac{828100x}{(-65x - 69)^{3}} + \frac{515450}{(-65x - 69)^{3}} - \frac{12740}{(-65x - 69)^{2}} - \frac{168}{(-65x - 69)}\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( \frac{-709800x^{2}}{(-65x - 69)^{3}} - \frac{21840x}{(-65x - 69)^{2}} - \frac{828100x}{(-65x - 69)^{3}} + \frac{515450}{(-65x - 69)^{3}} - \frac{12740}{(-65x - 69)^{2}} - \frac{168}{(-65x - 69)}\right)}{dx}\\=&-709800(\frac{-3(-65 + 0)}{(-65x - 69)^{4}})x^{2} - \frac{709800*2x}{(-65x - 69)^{3}} - 21840(\frac{-2(-65 + 0)}{(-65x - 69)^{3}})x - \frac{21840}{(-65x - 69)^{2}} - 828100(\frac{-3(-65 + 0)}{(-65x - 69)^{4}})x - \frac{828100}{(-65x - 69)^{3}} + 515450(\frac{-3(-65 + 0)}{(-65x - 69)^{4}}) - 12740(\frac{-2(-65 + 0)}{(-65x - 69)^{3}}) - 168(\frac{-(-65 + 0)}{(-65x - 69)^{2}})\\=&\frac{-138411000x^{2}}{(-65x - 69)^{4}} - \frac{4258800x}{(-65x - 69)^{3}} - \frac{161479500x}{(-65x - 69)^{4}} + \frac{100512750}{(-65x - 69)^{4}} - \frac{2484300}{(-65x - 69)^{3}} - \frac{32760}{(-65x - 69)^{2}}\\ \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!