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 1 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(x*0.1 + (1 - x)*0.19 - 0.08)}{sqrt(({x}^{2})({0.1}^{2}) + ({(1 - x)}^{2}){0.19}^{2} + 2*0.08x(1 - x)*0.1*0.19)} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{0.1x}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} + \frac{0.19}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.19x}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.08}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{0.1x}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} + \frac{0.19}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.19x}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.08}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)}\right)}{dx}\\=&\frac{0.1}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} + \frac{0.1x*-(0.1 - 0.19 + 0.00304 - 0.00304*2x + 0)*0.5}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.19*-(0.1 - 0.19 + 0.00304 - 0.00304*2x + 0)*0.5}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.19}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.19x*-(0.1 - 0.19 + 0.00304 - 0.00304*2x + 0)*0.5}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.08*-(0.1 - 0.19 + 0.00304 - 0.00304*2x + 0)*0.5}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}}\\=&\frac{0.1}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.005x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0095x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.000152x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.000304x^{2}}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0005776x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0095x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.01805x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0002888x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.19}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.0005776x^{2}}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.0002432x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.0095}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.01805}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.004}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.0076}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0001216}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.0002888}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(x*0.1 + (1 - x)*0.19 - 0.08)}{sqrt(({x}^{2})({0.1}^{2}) + ({(1 - x)}^{2}){0.19}^{2} + 2*0.08x(1 - x)*0.1*0.19)} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{0.1x}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} + \frac{0.19}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.19x}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.08}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{0.1x}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} + \frac{0.19}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.19x}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.08}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)}\right)}{dx}\\=&\frac{0.1}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} + \frac{0.1x*-(0.1 - 0.19 + 0.00304 - 0.00304*2x + 0)*0.5}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.19*-(0.1 - 0.19 + 0.00304 - 0.00304*2x + 0)*0.5}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.19}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.19x*-(0.1 - 0.19 + 0.00304 - 0.00304*2x + 0)*0.5}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.08*-(0.1 - 0.19 + 0.00304 - 0.00304*2x + 0)*0.5}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}}\\=&\frac{0.1}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.005x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0095x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.000152x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.000304x^{2}}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0005776x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0095x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.01805x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0002888x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.19}{sqrt(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)} - \frac{0.0005776x^{2}}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.0002432x}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.0095}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.01805}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.004}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.0076}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} + \frac{0.0001216}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}} - \frac{0.0002888}{(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)(0.1x - 0.19x + 0.00304x - 0.00304x^{2} + 0.19)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
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