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