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 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{2}^{{(x - {x}^{2})}^{\frac{1}{2}}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {2}^{(x - x^{2})^{\frac{1}{2}}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {2}^{(x - x^{2})^{\frac{1}{2}}}\right)}{dx}\\=&({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))\\=&\frac{-x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{1}{2}}}\right)}{dx}\\=&-(\frac{\frac{-1}{2}(1 - 2x)}{(x - x^{2})^{\frac{3}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} - \frac{x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{1}{2}}} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{1}{2}}(2)} + \frac{(\frac{\frac{-1}{2}(1 - 2x)}{(x - x^{2})^{\frac{3}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2} + \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{2(x - x^{2})^{\frac{1}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{2(x - x^{2})^{\frac{1}{2}}(2)}\\=&\frac{-x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} + \frac{x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{3}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} + \frac{x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{3}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})}\right)}{dx}\\=&-(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{3}{2}}(2)} + (\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{3}{2}}(2)} - (\frac{\frac{-1}{2}(1 - 2x)}{(x - x^{2})^{\frac{3}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{1}{2}}} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{1}{2}}(2)} + (\frac{-(1 - 2x)}{(x - x^{2})^{2}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2) + \frac{2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} + \frac{x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{(x - x^{2})} + \frac{x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{(x - x^{2})(2)} - (\frac{-(1 - 2x)}{(x - x^{2})^{2}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2) - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{(x - x^{2})} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{(x - x^{2})(2)} - \frac{(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4} - \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{4(x - x^{2})^{\frac{3}{2}}} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{4(x - x^{2})^{\frac{3}{2}}(2)} + \frac{(\frac{-(1 - 2x)}{(x - x^{2})^{2}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4} + \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{4(x - x^{2})} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{4(x - x^{2})(2)}\\=&\frac{-3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{5}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} - \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{2}} - \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{5}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})^{2}} + \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})} - \frac{x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{4(x - x^{2})^{\frac{3}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{8(x - x^{2})^{\frac{5}{2}}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{8(x - x^{2})^{2}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{8(x - x^{2})^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{5}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} - \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{2}} - \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{5}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})^{2}} + \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})} - \frac{x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{4(x - x^{2})^{\frac{3}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{8(x - x^{2})^{\frac{5}{2}}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{8(x - x^{2})^{2}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{8(x - x^{2})^{\frac{3}{2}}}\right)}{dx}\\=&-3(\frac{\frac{-5}{2}(1 - 2x)}{(x - x^{2})^{\frac{7}{2}}})x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{3*3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} - \frac{3x^{3}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{5}{2}}} - \frac{3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{5}{2}}(2)} + \frac{9(\frac{\frac{-5}{2}(1 - 2x)}{(x - x^{2})^{\frac{7}{2}}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2} + \frac{9*2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{5}{2}}} + \frac{9x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{2(x - x^{2})^{\frac{5}{2}}} + \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{2(x - x^{2})^{\frac{5}{2}}(2)} - 3(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{3x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{3}{2}}(2)} + 3(\frac{-2(1 - 2x)}{(x - x^{2})^{3}})x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2) + \frac{3*3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} + \frac{3x^{3}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{(x - x^{2})^{2}} + \frac{3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{(x - x^{2})^{2}(2)} - \frac{9(\frac{-2(1 - 2x)}{(x - x^{2})^{3}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2} - \frac{9*2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{2}} - \frac{9x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{2(x - x^{2})^{2}} - \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{2(x - x^{2})^{2}(2)} - \frac{9(\frac{\frac{-5}{2}(1 - 2x)}{(x - x^{2})^{\frac{7}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4} - \frac{9 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{5}{2}}} - \frac{9x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{4(x - x^{2})^{\frac{5}{2}}} - \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{4(x - x^{2})^{\frac{5}{2}}(2)} + \frac{3(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2} + \frac{3({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}*0}{2(x - x^{2})^{\frac{3}{2}}(2)} + \frac{9(\frac{-2(1 - 2x)}{(x - x^{2})^{3}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4} + \frac{9 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})^{2}} + \frac{9x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{4(x - x^{2})^{2}} + \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{4(x - x^{2})^{2}(2)} + 3(\frac{-(1 - 2x)}{(x - x^{2})^{2}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2) + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} + \frac{3x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{(x - x^{2})} + \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{(x - x^{2})(2)} - \frac{3(\frac{-(1 - 2x)}{(x - x^{2})^{2}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2} - \frac{3({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{2(x - x^{2})} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{2(x - x^{2})(2)} - (\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2) - \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{x^{3}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}*3ln^{2}(2)*0}{(x - x^{2})^{\frac{3}{2}}(2)} + \frac{3(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2} + \frac{3*2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*3ln^{2}(2)*0}{2(x - x^{2})^{\frac{3}{2}}(2)} - \frac{3(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{4} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{4(x - x^{2})^{\frac{3}{2}}} - \frac{3x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{3}(2)}{4(x - x^{2})^{\frac{3}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}*3ln^{2}(2)*0}{4(x - x^{2})^{\frac{3}{2}}(2)} + \frac{3(\frac{\frac{-5}{2}(1 - 2x)}{(x - x^{2})^{\frac{7}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{8} + \frac{3({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{8(x - x^{2})^{\frac{5}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}*0}{8(x - x^{2})^{\frac{5}{2}}(2)} - \frac{3(\frac{-2(1 - 2x)}{(x - x^{2})^{3}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{8} - \frac{3({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{8(x - x^{2})^{2}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{8(x - x^{2})^{2}(2)} + \frac{(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{8} + \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{3}(2)}{8(x - x^{2})^{\frac{3}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*3ln^{2}(2)*0}{8(x - x^{2})^{\frac{3}{2}}(2)}\\=&\frac{-15x^{4}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{7}{2}}} + \frac{30x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{7}{2}}} - \frac{18x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{15x^{4}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{3}} - \frac{30x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{3}} - \frac{45x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{7}{2}}} + \frac{18x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{45x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{3}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{18x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} - \frac{18x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} - \frac{6x^{4}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{12x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{6x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{15x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{7}{2}}} - \frac{9 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{5}{2}}} - \frac{15x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{3}} + \frac{9 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{2}} + \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{6x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{x^{4}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{(x - x^{2})^{2}} - \frac{2x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{(x - x^{2})^{2}} + \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{2(x - x^{2})^{2}} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{2(x - x^{2})^{2}} - \frac{15 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{16(x - x^{2})^{\frac{7}{2}}} + \frac{15 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{16(x - x^{2})^{3}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{8(x - x^{2})^{\frac{5}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{16(x - x^{2})^{2}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{2}^{{(x - {x}^{2})}^{\frac{1}{2}}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {2}^{(x - x^{2})^{\frac{1}{2}}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {2}^{(x - x^{2})^{\frac{1}{2}}}\right)}{dx}\\=&({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))\\=&\frac{-x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{1}{2}}}\right)}{dx}\\=&-(\frac{\frac{-1}{2}(1 - 2x)}{(x - x^{2})^{\frac{3}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} - \frac{x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{1}{2}}} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{1}{2}}(2)} + \frac{(\frac{\frac{-1}{2}(1 - 2x)}{(x - x^{2})^{\frac{3}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2} + \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{2(x - x^{2})^{\frac{1}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{2(x - x^{2})^{\frac{1}{2}}(2)}\\=&\frac{-x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} + \frac{x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{3}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{1}{2}}} + \frac{x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{3}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})}\right)}{dx}\\=&-(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{3}{2}}(2)} + (\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{3}{2}}(2)} - (\frac{\frac{-1}{2}(1 - 2x)}{(x - x^{2})^{\frac{3}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{1}{2}}} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{1}{2}}(2)} + (\frac{-(1 - 2x)}{(x - x^{2})^{2}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2) + \frac{2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} + \frac{x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{(x - x^{2})} + \frac{x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{(x - x^{2})(2)} - (\frac{-(1 - 2x)}{(x - x^{2})^{2}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2) - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{(x - x^{2})} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{(x - x^{2})(2)} - \frac{(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4} - \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{4(x - x^{2})^{\frac{3}{2}}} - \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{4(x - x^{2})^{\frac{3}{2}}(2)} + \frac{(\frac{-(1 - 2x)}{(x - x^{2})^{2}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4} + \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{4(x - x^{2})} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{4(x - x^{2})(2)}\\=&\frac{-3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{5}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} - \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{2}} - \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{5}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})^{2}} + \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})} - \frac{x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{4(x - x^{2})^{\frac{3}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{8(x - x^{2})^{\frac{5}{2}}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{8(x - x^{2})^{2}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{8(x - x^{2})^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{5}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} - \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{2}} - \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{5}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})^{2}} + \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})} - \frac{x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{4(x - x^{2})^{\frac{3}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{8(x - x^{2})^{\frac{5}{2}}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{8(x - x^{2})^{2}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{8(x - x^{2})^{\frac{3}{2}}}\right)}{dx}\\=&-3(\frac{\frac{-5}{2}(1 - 2x)}{(x - x^{2})^{\frac{7}{2}}})x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{3*3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} - \frac{3x^{3}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{5}{2}}} - \frac{3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{5}{2}}(2)} + \frac{9(\frac{\frac{-5}{2}(1 - 2x)}{(x - x^{2})^{\frac{7}{2}}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2} + \frac{9*2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{5}{2}}} + \frac{9x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{2(x - x^{2})^{\frac{5}{2}}} + \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{2(x - x^{2})^{\frac{5}{2}}(2)} - 3(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2) - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{3x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{(x - x^{2})^{\frac{3}{2}}(2)} + 3(\frac{-2(1 - 2x)}{(x - x^{2})^{3}})x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2) + \frac{3*3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} + \frac{3x^{3}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{(x - x^{2})^{2}} + \frac{3x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{(x - x^{2})^{2}(2)} - \frac{9(\frac{-2(1 - 2x)}{(x - x^{2})^{3}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2} - \frac{9*2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{2}} - \frac{9x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{2(x - x^{2})^{2}} - \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{2(x - x^{2})^{2}(2)} - \frac{9(\frac{\frac{-5}{2}(1 - 2x)}{(x - x^{2})^{\frac{7}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4} - \frac{9 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{4(x - x^{2})^{\frac{5}{2}}} - \frac{9x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{4(x - x^{2})^{\frac{5}{2}}} - \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}*0}{4(x - x^{2})^{\frac{5}{2}}(2)} + \frac{3(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2} + \frac{3({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}*0}{2(x - x^{2})^{\frac{3}{2}}(2)} + \frac{9(\frac{-2(1 - 2x)}{(x - x^{2})^{3}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4} + \frac{9 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{4(x - x^{2})^{2}} + \frac{9x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{4(x - x^{2})^{2}} + \frac{9x{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{4(x - x^{2})^{2}(2)} + 3(\frac{-(1 - 2x)}{(x - x^{2})^{2}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2) + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} + \frac{3x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{(x - x^{2})} + \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{(x - x^{2})(2)} - \frac{3(\frac{-(1 - 2x)}{(x - x^{2})^{2}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2} - \frac{3({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{2(x - x^{2})} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{2(x - x^{2})(2)} - (\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2) - \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{x^{3}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}*3ln^{2}(2)*0}{(x - x^{2})^{\frac{3}{2}}(2)} + \frac{3(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2} + \frac{3*2x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{2}({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}*3ln^{2}(2)*0}{2(x - x^{2})^{\frac{3}{2}}(2)} - \frac{3(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}})x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{4} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{4(x - x^{2})^{\frac{3}{2}}} - \frac{3x({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{3}(2)}{4(x - x^{2})^{\frac{3}{2}}} - \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}*3ln^{2}(2)*0}{4(x - x^{2})^{\frac{3}{2}}(2)} + \frac{3(\frac{\frac{-5}{2}(1 - 2x)}{(x - x^{2})^{\frac{7}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{8} + \frac{3({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln(2)}{8(x - x^{2})^{\frac{5}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}*0}{8(x - x^{2})^{\frac{5}{2}}(2)} - \frac{3(\frac{-2(1 - 2x)}{(x - x^{2})^{3}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{8} - \frac{3({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{2}(2)}{8(x - x^{2})^{2}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}*2ln(2)*0}{8(x - x^{2})^{2}(2)} + \frac{(\frac{\frac{-3}{2}(1 - 2x)}{(x - x^{2})^{\frac{5}{2}}}){2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{8} + \frac{({2}^{(x - x^{2})^{\frac{1}{2}}}(((\frac{\frac{1}{2}(1 - 2x)}{(x - x^{2})^{\frac{1}{2}}}))ln(2) + \frac{((x - x^{2})^{\frac{1}{2}})(0)}{(2)}))ln^{3}(2)}{8(x - x^{2})^{\frac{3}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}*3ln^{2}(2)*0}{8(x - x^{2})^{\frac{3}{2}}(2)}\\=&\frac{-15x^{4}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{7}{2}}} + \frac{30x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{7}{2}}} - \frac{18x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{15x^{4}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{3}} - \frac{30x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{3}} - \frac{45x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{7}{2}}} + \frac{18x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{45x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{3}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{(x - x^{2})^{\frac{3}{2}}} + \frac{18x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} - \frac{18x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})^{2}} - \frac{6x^{4}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{12x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{6x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{9x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{15x{2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{7}{2}}} - \frac{9 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{2(x - x^{2})^{\frac{5}{2}}} - \frac{15x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{3}} + \frac{9 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{2(x - x^{2})^{2}} + \frac{3x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{5}{2}}} + \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{(x - x^{2})} - \frac{6x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{(x - x^{2})^{\frac{3}{2}}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{2(x - x^{2})^{\frac{3}{2}}} + \frac{x^{4}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{(x - x^{2})^{2}} - \frac{2x^{3}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{(x - x^{2})^{2}} + \frac{3x^{2}{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{2(x - x^{2})^{2}} - \frac{x{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{2(x - x^{2})^{2}} - \frac{15 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln(2)}{16(x - x^{2})^{\frac{7}{2}}} + \frac{15 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{2}(2)}{16(x - x^{2})^{3}} - \frac{3 * {2}^{(x - x^{2})^{\frac{1}{2}}}ln^{3}(2)}{8(x - x^{2})^{\frac{5}{2}}} + \frac{{2}^{(x - x^{2})^{\frac{1}{2}}}ln^{4}(2)}{16(x - x^{2})^{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。