求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{x}{((2000a + 3200pix + ax)(b + x))} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\right)}{dx}\\=&(\frac{-(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}})x + \frac{1}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\\=&\frac{-abx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{2ax^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{3200pibx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{6400pix^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{2000ax}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{1}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-abx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{2ax^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{3200pibx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{6400pix^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{2000ax}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{1}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\right)}{dx}\\=&-(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})abx - \frac{ab}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - 2(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})ax^{2} - \frac{2a*2x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - 3200(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})pibx - \frac{3200pib}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - 6400(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})pix^{2} - \frac{6400pi*2x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - 2000(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})ax - \frac{2000a}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + (\frac{-(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}})\\=&\frac{2a^{2}b^{2}x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{8a^{2}bx^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{12800apib^{2}x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{51200apibx^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{8000a^{2}bx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{2ab}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{8a^{2}x^{3}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{51200apix^{3}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{16000a^{2}x^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{6ax}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{20480000p^{2}i^{2}b^{2}x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{81920000p^{2}i^{2}bx^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{25600000apibx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{6400pib}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{81920000p^{2}i^{2}x^{3}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{51200000apix^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{19200pix}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{8000000a^{2}x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{4000a}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{x}{((2000a + 3200pix + ax)(b + x))} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\right)}{dx}\\=&(\frac{-(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}})x + \frac{1}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\\=&\frac{-abx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{2ax^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{3200pibx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{6400pix^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{2000ax}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{1}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-abx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{2ax^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{3200pibx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{6400pix^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - \frac{2000ax}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{1}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)}\right)}{dx}\\=&-(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})abx - \frac{ab}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - 2(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})ax^{2} - \frac{2a*2x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - 3200(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})pibx - \frac{3200pib}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - 6400(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})pix^{2} - \frac{6400pi*2x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} - 2000(\frac{-2(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}})ax - \frac{2000a}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + (\frac{-(ab + a*2x + 3200pib + 3200pi*2x + 0 + 2000a)}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}})\\=&\frac{2a^{2}b^{2}x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{8a^{2}bx^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{12800apib^{2}x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{51200apibx^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{8000a^{2}bx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{2ab}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{8a^{2}x^{3}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{51200apix^{3}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{16000a^{2}x^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{6ax}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{20480000p^{2}i^{2}b^{2}x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{81920000p^{2}i^{2}bx^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{25600000apibx}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{6400pib}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{81920000p^{2}i^{2}x^{3}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} + \frac{51200000apix^{2}}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{19200pix}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{2}} + \frac{8000000a^{2}x}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{3}} - \frac{4000a}{(abx + ax^{2} + 3200pibx + 3200pix^{2} + 2000ab + 2000ax)^{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！
最 新 发 布
新增加身体健康评估计算器，位置：“数学运算 > 身体健康评估”。
新增加学习笔记(安卓版)百度网盘快速下载应用程序，欢迎使用。
新增加学习笔记(安卓版)本站下载应用程序，欢迎使用。
新增线性代数行列式的计算，欢迎使用。
数学计算和一元方程已经支持正割函数和余割函数，欢迎使用。
新增加贷款计算器模块（具体位置：数学运算 > 贷款计算器），欢迎使用。