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。\[ \begin{equation}\begin{split}【1/1】求函数(2m{x}^{(2m - 1)} - 1)({x}^{(2n)} - 1) - 2n{x}^{(2n - 1)}({x}^{(2m)} - x) 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 2m{x}^{(2m - 1)}{x}^{(2n)} - 2m{x}^{(2m - 1)} - {x}^{(2n)} - 2n{x}^{(2n - 1)}{x}^{(2m)} + 2nx{x}^{(2n - 1)} + 1\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( 2m{x}^{(2m - 1)}{x}^{(2n)} - 2m{x}^{(2m - 1)} - {x}^{(2n)} - 2n{x}^{(2n - 1)}{x}^{(2m)} + 2nx{x}^{(2n - 1)} + 1\right)}{dx}\\=&2m({x}^{(2m - 1)}((0 + 0)ln(x) + \frac{(2m - 1)(1)}{(x)})){x}^{(2n)} + 2m{x}^{(2m - 1)}({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)})) - 2m({x}^{(2m - 1)}((0 + 0)ln(x) + \frac{(2m - 1)(1)}{(x)})) - ({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)})) - 2n({x}^{(2n - 1)}((0 + 0)ln(x) + \frac{(2n - 1)(1)}{(x)})){x}^{(2m)} - 2n{x}^{(2n - 1)}({x}^{(2m)}((0)ln(x) + \frac{(2m)(1)}{(x)})) + 2n{x}^{(2n - 1)} + 2nx({x}^{(2n - 1)}((0 + 0)ln(x) + \frac{(2n - 1)(1)}{(x)})) + 0\\=&\frac{4m^{2}{x}^{(2m - 1)}{x}^{(2n)}}{x} - \frac{2m{x}^{(2m - 1)}{x}^{(2n)}}{x} + \frac{4mn{x}^{(2n)}{x}^{(2m - 1)}}{x} - \frac{4m^{2}{x}^{(2m - 1)}}{x} + \frac{2m{x}^{(2m - 1)}}{x} - \frac{4n^{2}{x}^{(2n - 1)}{x}^{(2m)}}{x} + \frac{2n{x}^{(2n - 1)}{x}^{(2m)}}{x} - \frac{4mn{x}^{(2m)}{x}^{(2n - 1)}}{x} - \frac{2n{x}^{(2n)}}{x} + 4n^{2}{x}^{(2n - 1)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{4m^{2}{x}^{(2m - 1)}{x}^{(2n)}}{x} - \frac{2m{x}^{(2m - 1)}{x}^{(2n)}}{x} + \frac{4mn{x}^{(2n)}{x}^{(2m - 1)}}{x} - \frac{4m^{2}{x}^{(2m - 1)}}{x} + \frac{2m{x}^{(2m - 1)}}{x} - \frac{4n^{2}{x}^{(2n - 1)}{x}^{(2m)}}{x} + \frac{2n{x}^{(2n - 1)}{x}^{(2m)}}{x} - \frac{4mn{x}^{(2m)}{x}^{(2n - 1)}}{x} - \frac{2n{x}^{(2n)}}{x} + 4n^{2}{x}^{(2n - 1)}\right)}{dx}\\=&\frac{4m^{2}*-{x}^{(2m - 1)}{x}^{(2n)}}{x^{2}} + \frac{4m^{2}({x}^{(2m - 1)}((0 + 0)ln(x) + \frac{(2m - 1)(1)}{(x)})){x}^{(2n)}}{x} + \frac{4m^{2}{x}^{(2m - 1)}({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)}))}{x} - \frac{2m*-{x}^{(2m - 1)}{x}^{(2n)}}{x^{2}} - \frac{2m({x}^{(2m - 1)}((0 + 0)ln(x) + \frac{(2m - 1)(1)}{(x)})){x}^{(2n)}}{x} - \frac{2m{x}^{(2m - 1)}({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)}))}{x} + \frac{4mn*-{x}^{(2n)}{x}^{(2m - 1)}}{x^{2}} + \frac{4mn({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)})){x}^{(2m - 1)}}{x} + \frac{4mn{x}^{(2n)}({x}^{(2m - 1)}((0 + 0)ln(x) + \frac{(2m - 1)(1)}{(x)}))}{x} - \frac{4m^{2}*-{x}^{(2m - 1)}}{x^{2}} - \frac{4m^{2}({x}^{(2m - 1)}((0 + 0)ln(x) + \frac{(2m - 1)(1)}{(x)}))}{x} + \frac{2m*-{x}^{(2m - 1)}}{x^{2}} + \frac{2m({x}^{(2m - 1)}((0 + 0)ln(x) + \frac{(2m - 1)(1)}{(x)}))}{x} - \frac{4n^{2}*-{x}^{(2n - 1)}{x}^{(2m)}}{x^{2}} - \frac{4n^{2}({x}^{(2n - 1)}((0 + 0)ln(x) + \frac{(2n - 1)(1)}{(x)})){x}^{(2m)}}{x} - \frac{4n^{2}{x}^{(2n - 1)}({x}^{(2m)}((0)ln(x) + \frac{(2m)(1)}{(x)}))}{x} + \frac{2n*-{x}^{(2n - 1)}{x}^{(2m)}}{x^{2}} + \frac{2n({x}^{(2n - 1)}((0 + 0)ln(x) + \frac{(2n - 1)(1)}{(x)})){x}^{(2m)}}{x} + \frac{2n{x}^{(2n - 1)}({x}^{(2m)}((0)ln(x) + \frac{(2m)(1)}{(x)}))}{x} - \frac{4mn*-{x}^{(2m)}{x}^{(2n - 1)}}{x^{2}} - \frac{4mn({x}^{(2m)}((0)ln(x) + \frac{(2m)(1)}{(x)})){x}^{(2n - 1)}}{x} - \frac{4mn{x}^{(2m)}({x}^{(2n - 1)}((0 + 0)ln(x) + \frac{(2n - 1)(1)}{(x)}))}{x} - \frac{2n*-{x}^{(2n)}}{x^{2}} - \frac{2n({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)}))}{x} + 4n^{2}({x}^{(2n - 1)}((0 + 0)ln(x) + \frac{(2n - 1)(1)}{(x)}))\\=&\frac{-12m^{2}{x}^{(2m - 1)}{x}^{(2n)}}{x^{2}} + \frac{8m^{3}{x}^{(2m - 1)}{x}^{(2n)}}{x^{2}} + \frac{8m^{2}n{x}^{(2n)}{x}^{(2m - 1)}}{x^{2}} + \frac{4m{x}^{(2m - 1)}{x}^{(2n)}}{x^{2}} - \frac{8mn{x}^{(2n)}{x}^{(2m - 1)}}{x^{2}} + \frac{8mn^{2}{x}^{(2n)}{x}^{(2m - 1)}}{x^{2}} + \frac{8m^{2}n{x}^{(2m - 1)}{x}^{(2n)}}{x^{2}} - \frac{4mn{x}^{(2m - 1)}{x}^{(2n)}}{x^{2}} + \frac{12m^{2}{x}^{(2m - 1)}}{x^{2}} - \frac{8m^{3}{x}^{(2m - 1)}}{x^{2}} - \frac{4m{x}^{(2m - 1)}}{x^{2}} + \frac{12n^{2}{x}^{(2n - 1)}{x}^{(2m)}}{x^{2}} - \frac{8n^{3}{x}^{(2n - 1)}{x}^{(2m)}}{x^{2}} - \frac{8mn^{2}{x}^{(2m)}{x}^{(2n - 1)}}{x^{2}} - \frac{4n{x}^{(2n - 1)}{x}^{(2m)}}{x^{2}} + \frac{8mn{x}^{(2m)}{x}^{(2n - 1)}}{x^{2}} - \frac{8m^{2}n{x}^{(2m)}{x}^{(2n - 1)}}{x^{2}} - \frac{8mn^{2}{x}^{(2n - 1)}{x}^{(2m)}}{x^{2}} + \frac{4mn{x}^{(2n - 1)}{x}^{(2m)}}{x^{2}} + \frac{2n{x}^{(2n)}}{x^{2}} - \frac{4n^{2}{x}^{(2n)}}{x^{2}} + \frac{8n^{3}{x}^{(2n - 1)}}{x} - \frac{4n^{2}{x}^{(2n - 1)}}{x}\\ \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!