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。\[ \begin{equation}\begin{split}【1/1】求函数{(\frac{(x - 1)(x - 2)}{((x - 3)(x - 4))})}^{\frac{1}{2}} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}}{(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}}{(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{(\frac{\frac{1}{2}(1 + 0)}{(x - 1)^{\frac{1}{2}}})(x - 2)^{\frac{1}{2}}}{(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}} + \frac{(x - 1)^{\frac{1}{2}}(\frac{\frac{1}{2}(1 + 0)}{(x - 2)^{\frac{1}{2}}})}{(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}} + \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}(\frac{\frac{-1}{2}(1 + 0)}{(x - 3)^{\frac{3}{2}}})}{(x - 4)^{\frac{1}{2}}} + \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}(\frac{\frac{-1}{2}(1 + 0)}{(x - 4)^{\frac{3}{2}}})}{(x - 3)^{\frac{1}{2}}}\\=&\frac{(x - 2)^{\frac{1}{2}}}{2(x - 1)^{\frac{1}{2}}(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}} + \frac{(x - 1)^{\frac{1}{2}}}{2(x - 2)^{\frac{1}{2}}(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}} - \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}}{2(x - 3)^{\frac{3}{2}}(x - 4)^{\frac{1}{2}}} - \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}}{2(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!