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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{(100 + 2*100 - 2x)(100 + x)}{(10000 + 100*100 - 100x)} - 1 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{100x}{(-100x + 20000)} - \frac{2x^{2}}{(-100x + 20000)} + \frac{30000}{(-100x + 20000)} - 1\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{100x}{(-100x + 20000)} - \frac{2x^{2}}{(-100x + 20000)} + \frac{30000}{(-100x + 20000)} - 1\right)}{dx}\\=&100(\frac{-(-100 + 0)}{(-100x + 20000)^{2}})x + \frac{100}{(-100x + 20000)} - 2(\frac{-(-100 + 0)}{(-100x + 20000)^{2}})x^{2} - \frac{2*2x}{(-100x + 20000)} + 30000(\frac{-(-100 + 0)}{(-100x + 20000)^{2}}) + 0\\=&\frac{10000x}{(-100x + 20000)^{2}} - \frac{200x^{2}}{(-100x + 20000)^{2}} - \frac{4x}{(-100x + 20000)} + \frac{3000000}{(-100x + 20000)^{2}} + \frac{100}{(-100x + 20000)}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!