本次共计算 1 个题目:每一题对 x 求 2 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数(6{x}^{2} + 6x){\frac{1}{({x}^{2} + x + 1)}}^{3} 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{6x^{2}}{(x^{2} + x + 1)^{3}} + \frac{6x}{(x^{2} + x + 1)^{3}}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{6x^{2}}{(x^{2} + x + 1)^{3}} + \frac{6x}{(x^{2} + x + 1)^{3}}\right)}{dx}\\=&6(\frac{-3(2x + 1 + 0)}{(x^{2} + x + 1)^{4}})x^{2} + \frac{6*2x}{(x^{2} + x + 1)^{3}} + 6(\frac{-3(2x + 1 + 0)}{(x^{2} + x + 1)^{4}})x + \frac{6}{(x^{2} + x + 1)^{3}}\\=&\frac{-36x^{3}}{(x^{2} + x + 1)^{4}} - \frac{54x^{2}}{(x^{2} + x + 1)^{4}} + \frac{12x}{(x^{2} + x + 1)^{3}} - \frac{18x}{(x^{2} + x + 1)^{4}} + \frac{6}{(x^{2} + x + 1)^{3}}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{-36x^{3}}{(x^{2} + x + 1)^{4}} - \frac{54x^{2}}{(x^{2} + x + 1)^{4}} + \frac{12x}{(x^{2} + x + 1)^{3}} - \frac{18x}{(x^{2} + x + 1)^{4}} + \frac{6}{(x^{2} + x + 1)^{3}}\right)}{dx}\\=&-36(\frac{-4(2x + 1 + 0)}{(x^{2} + x + 1)^{5}})x^{3} - \frac{36*3x^{2}}{(x^{2} + x + 1)^{4}} - 54(\frac{-4(2x + 1 + 0)}{(x^{2} + x + 1)^{5}})x^{2} - \frac{54*2x}{(x^{2} + x + 1)^{4}} + 12(\frac{-3(2x + 1 + 0)}{(x^{2} + x + 1)^{4}})x + \frac{12}{(x^{2} + x + 1)^{3}} - 18(\frac{-4(2x + 1 + 0)}{(x^{2} + x + 1)^{5}})x - \frac{18}{(x^{2} + x + 1)^{4}} + 6(\frac{-3(2x + 1 + 0)}{(x^{2} + x + 1)^{4}})\\=&\frac{288x^{4}}{(x^{2} + x + 1)^{5}} + \frac{576x^{3}}{(x^{2} + x + 1)^{5}} - \frac{180x^{2}}{(x^{2} + x + 1)^{4}} + \frac{360x^{2}}{(x^{2} + x + 1)^{5}} - \frac{180x}{(x^{2} + x + 1)^{4}} + \frac{72x}{(x^{2} + x + 1)^{5}} - \frac{36}{(x^{2} + x + 1)^{4}} + \frac{12}{(x^{2} + x + 1)^{3}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!