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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{x}{sqrt({x}^{(2 + {x}^{2})})} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x}{sqrt({x}^{(x^{2} + 2)})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x}{sqrt({x}^{(x^{2} + 2)})}\right)}{dx}\\=&\frac{1}{sqrt({x}^{(x^{2} + 2)})} + \frac{x*-({x}^{(x^{2} + 2)}((2x + 0)ln(x) + \frac{(x^{2} + 2)(1)}{(x)}))*\frac{1}{2}}{({x}^{(x^{2} + 2)})({x}^{(x^{2} + 2)})^{\frac{1}{2}}}\\=&\frac{1}{sqrt({x}^{(x^{2} + 2)})} - x^{2}{x}^{(2x^{2} + 4)}ln(x) - \frac{x^{2}{x}^{(2x^{2} + 4)}}{2} - {x}^{(2x^{2} + 4)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{sqrt({x}^{(x^{2} + 2)})} - x^{2}{x}^{(2x^{2} + 4)}ln(x) - \frac{x^{2}{x}^{(2x^{2} + 4)}}{2} - {x}^{(2x^{2} + 4)}\right)}{dx}\\=&\frac{-({x}^{(x^{2} + 2)}((2x + 0)ln(x) + \frac{(x^{2} + 2)(1)}{(x)}))*\frac{1}{2}}{({x}^{(x^{2} + 2)})({x}^{(x^{2} + 2)})^{\frac{1}{2}}} - 2x{x}^{(2x^{2} + 4)}ln(x) - x^{2}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln(x) - \frac{x^{2}{x}^{(2x^{2} + 4)}}{(x)} - \frac{2x{x}^{(2x^{2} + 4)}}{2} - \frac{x^{2}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))}{2} - ({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))\\=&-11x{x}^{(2x^{2} + 4)}ln(x) - 4x^{3}{x}^{(2x^{2} + 4)}ln^{2}(x) - 4x^{3}{x}^{(2x^{2} + 4)}ln(x) - \frac{5{x}^{(2x^{2} + 4)}}{x} - \frac{13x{x}^{(2x^{2} + 4)}}{2} - x^{3}{x}^{(2x^{2} + 4)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -11x{x}^{(2x^{2} + 4)}ln(x) - 4x^{3}{x}^{(2x^{2} + 4)}ln^{2}(x) - 4x^{3}{x}^{(2x^{2} + 4)}ln(x) - \frac{5{x}^{(2x^{2} + 4)}}{x} - \frac{13x{x}^{(2x^{2} + 4)}}{2} - x^{3}{x}^{(2x^{2} + 4)}\right)}{dx}\\=&-11{x}^{(2x^{2} + 4)}ln(x) - 11x({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln(x) - \frac{11x{x}^{(2x^{2} + 4)}}{(x)} - 4*3x^{2}{x}^{(2x^{2} + 4)}ln^{2}(x) - 4x^{3}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln^{2}(x) - \frac{4x^{3}{x}^{(2x^{2} + 4)}*2ln(x)}{(x)} - 4*3x^{2}{x}^{(2x^{2} + 4)}ln(x) - 4x^{3}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln(x) - \frac{4x^{3}{x}^{(2x^{2} + 4)}}{(x)} - \frac{5*-{x}^{(2x^{2} + 4)}}{x^{2}} - \frac{5({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))}{x} - \frac{13{x}^{(2x^{2} + 4)}}{2} - \frac{13x({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))}{2} - 3x^{2}{x}^{(2x^{2} + 4)} - x^{3}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))\\=&-75{x}^{(2x^{2} + 4)}ln(x) - 72x^{2}{x}^{(2x^{2} + 4)}ln^{2}(x) - 84x^{2}{x}^{(2x^{2} + 4)}ln(x) - \frac{107{x}^{(2x^{2} + 4)}}{2} - 16x^{4}{x}^{(2x^{2} + 4)}ln^{3}(x) - 24x^{4}{x}^{(2x^{2} + 4)}ln^{2}(x) - 12x^{4}{x}^{(2x^{2} + 4)}ln(x) - 24x^{2}{x}^{(2x^{2} + 4)} - \frac{15{x}^{(2x^{2} + 4)}}{x^{2}} - 2x^{4}{x}^{(2x^{2} + 4)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -75{x}^{(2x^{2} + 4)}ln(x) - 72x^{2}{x}^{(2x^{2} + 4)}ln^{2}(x) - 84x^{2}{x}^{(2x^{2} + 4)}ln(x) - \frac{107{x}^{(2x^{2} + 4)}}{2} - 16x^{4}{x}^{(2x^{2} + 4)}ln^{3}(x) - 24x^{4}{x}^{(2x^{2} + 4)}ln^{2}(x) - 12x^{4}{x}^{(2x^{2} + 4)}ln(x) - 24x^{2}{x}^{(2x^{2} + 4)} - \frac{15{x}^{(2x^{2} + 4)}}{x^{2}} - 2x^{4}{x}^{(2x^{2} + 4)}\right)}{dx}\\=&-75({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln(x) - \frac{75{x}^{(2x^{2} + 4)}}{(x)} - 72*2x{x}^{(2x^{2} + 4)}ln^{2}(x) - 72x^{2}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln^{2}(x) - \frac{72x^{2}{x}^{(2x^{2} + 4)}*2ln(x)}{(x)} - 84*2x{x}^{(2x^{2} + 4)}ln(x) - 84x^{2}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln(x) - \frac{84x^{2}{x}^{(2x^{2} + 4)}}{(x)} - \frac{107({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))}{2} - 16*4x^{3}{x}^{(2x^{2} + 4)}ln^{3}(x) - 16x^{4}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln^{3}(x) - \frac{16x^{4}{x}^{(2x^{2} + 4)}*3ln^{2}(x)}{(x)} - 24*4x^{3}{x}^{(2x^{2} + 4)}ln^{2}(x) - 24x^{4}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln^{2}(x) - \frac{24x^{4}{x}^{(2x^{2} + 4)}*2ln(x)}{(x)} - 12*4x^{3}{x}^{(2x^{2} + 4)}ln(x) - 12x^{4}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))ln(x) - \frac{12x^{4}{x}^{(2x^{2} + 4)}}{(x)} - 24*2x{x}^{(2x^{2} + 4)} - 24x^{2}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)})) - \frac{15*-2{x}^{(2x^{2} + 4)}}{x^{3}} - \frac{15({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))}{x^{2}} - 2*4x^{3}{x}^{(2x^{2} + 4)} - 2x^{4}({x}^{(2x^{2} + 4)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 4)(1)}{(x)}))\\=&-732x{x}^{(2x^{2} + 4)}ln^{2}(x) - 1012x{x}^{(2x^{2} + 4)}ln(x) - \frac{360{x}^{(2x^{2} + 4)}ln(x)}{x} - 416x^{3}{x}^{(2x^{2} + 4)}ln^{3}(x) - 720x^{3}{x}^{(2x^{2} + 4)}ln^{2}(x) - 408x^{3}{x}^{(2x^{2} + 4)}ln(x) - 64x^{5}{x}^{(2x^{2} + 4)}ln^{4}(x) - 128x^{5}{x}^{(2x^{2} + 4)}ln^{3}(x) - 96x^{5}{x}^{(2x^{2} + 4)}ln^{2}(x) - 32x^{5}{x}^{(2x^{2} + 4)}ln(x) - \frac{319{x}^{(2x^{2} + 4)}}{x} - 335x{x}^{(2x^{2} + 4)} - 76x^{3}{x}^{(2x^{2} + 4)} - \frac{30{x}^{(2x^{2} + 4)}}{x^{3}} - 4x^{5}{x}^{(2x^{2} + 4)}\\ \end{split}\end{equation} \]