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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{{(\frac{1}{2} - x)}^{(\frac{(n + 1)}{n})}(2nx + n + 1)}{(2n + 1)} - \frac{((n + 1)dr{x}^{\frac{1}{n}})}{(2n{(c{r}^{2} + 1)}^{2})} + \frac{(n + 1)alpha}{(n(c{r}^{2} + 1))} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{2nx(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)} + \frac{n(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)} + \frac{(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)} - \frac{\frac{1}{2}dr{x}^{\frac{1}{n}}}{(r^{2}c + 1)^{2}} - \frac{\frac{1}{2}dr{x}^{\frac{1}{n}}}{(r^{2}c + 1)^{2}n} + \frac{na^{2}lph}{(nr^{2}c + n)} + \frac{a^{2}lph}{(nr^{2}c + n)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{2nx(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)} + \frac{n(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)} + \frac{(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)} - \frac{\frac{1}{2}dr{x}^{\frac{1}{n}}}{(r^{2}c + 1)^{2}} - \frac{\frac{1}{2}dr{x}^{\frac{1}{n}}}{(r^{2}c + 1)^{2}n} + \frac{na^{2}lph}{(nr^{2}c + n)} + \frac{a^{2}lph}{(nr^{2}c + n)}\right)}{dx}\\=&2(\frac{-(0 + 0)}{(2n + 1)^{2}})nx(-x + \frac{1}{2})^{(\frac{1}{n} + 1)} + \frac{2n(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)} + \frac{2nx((-x + \frac{1}{2})^{(\frac{1}{n} + 1)}((0 + 0)ln(-x + \frac{1}{2}) + \frac{(\frac{1}{n} + 1)(-1 + 0)}{(-x + \frac{1}{2})}))}{(2n + 1)} + (\frac{-(0 + 0)}{(2n + 1)^{2}})n(-x + \frac{1}{2})^{(\frac{1}{n} + 1)} + \frac{n((-x + \frac{1}{2})^{(\frac{1}{n} + 1)}((0 + 0)ln(-x + \frac{1}{2}) + \frac{(\frac{1}{n} + 1)(-1 + 0)}{(-x + \frac{1}{2})}))}{(2n + 1)} + (\frac{-(0 + 0)}{(2n + 1)^{2}})(-x + \frac{1}{2})^{(\frac{1}{n} + 1)} + \frac{((-x + \frac{1}{2})^{(\frac{1}{n} + 1)}((0 + 0)ln(-x + \frac{1}{2}) + \frac{(\frac{1}{n} + 1)(-1 + 0)}{(-x + \frac{1}{2})}))}{(2n + 1)} - \frac{1}{2}(\frac{-2(0 + 0)}{(r^{2}c + 1)^{3}})dr{x}^{\frac{1}{n}} - \frac{\frac{1}{2}dr({x}^{\frac{1}{n}}((0)ln(x) + \frac{(\frac{1}{n})(1)}{(x)}))}{(r^{2}c + 1)^{2}} - \frac{\frac{1}{2}(\frac{-2(0 + 0)}{(r^{2}c + 1)^{3}})dr{x}^{\frac{1}{n}}}{n} - \frac{\frac{1}{2}dr({x}^{\frac{1}{n}}((0)ln(x) + \frac{(\frac{1}{n})(1)}{(x)}))}{(r^{2}c + 1)^{2}n} + (\frac{-(0 + 0)}{(nr^{2}c + n)^{2}})na^{2}lph + 0 + (\frac{-(0 + 0)}{(nr^{2}c + n)^{2}})a^{2}lph + 0\\=&\frac{2n(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)} - \frac{2x(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)(-x + \frac{1}{2})} - \frac{2nx(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)(-x + \frac{1}{2})} - \frac{2(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)(-x + \frac{1}{2})} - \frac{n(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)(-x + \frac{1}{2})} - \frac{(-x + \frac{1}{2})^{(\frac{1}{n} + 1)}}{(2n + 1)(-x + \frac{1}{2})n} - \frac{dr{x}^{\frac{1}{n}}}{2(r^{2}c + 1)^{2}nx} - \frac{dr{x}^{\frac{1}{n}}}{2(r^{2}c + 1)^{2}n^{2}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!