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。
\[ \begin{equation}\begin{split}【1/1】求函数sin({({x}^{2})}^{{x}^{2}}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin({x^{2}}^{x^{2}})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin({x^{2}}^{x^{2}})\right)}{dx}\\=&cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&2x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 2x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 2x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})\right)}{dx}\\=&2{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 2x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{2x{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 2x{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 2{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 2x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 2x{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&2{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 6{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 8x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}})\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 6{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 8x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}})\right)}{dx}\\=&2({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{2{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 2{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 4*2x{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 4x^{2}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{4x^{2}{x^{2}}^{x^{2}}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 4x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 8*2x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{2}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{8x^{2}{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 8x^{2}{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 6({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 6{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 4*2x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 4x^{2}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{4x^{2}{x^{2}}^{(2x^{2})}*2ln(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 4x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 8*2x{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 8x^{2}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{8x^{2}{x^{2}}^{(2x^{2})}*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 8x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 4*2x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 4x^{2}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 4*2x{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 4x^{2}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))sin({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&12x{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 48x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{4{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x} - 12x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 48x{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 36x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 36x{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}})\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 12x{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 48x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{4{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x} - 12x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 48x{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 36x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 36x{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}})\right)}{dx}\\=&12{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 12x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{12x{x^{2}}^{x^{2}}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 12x{x^{2}}^{x^{2}}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 48{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 48x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{48x{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 48x{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + \frac{4*-{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x^{2}} + \frac{4({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}})}{x} + \frac{4{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))}{x} - 12{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 12x({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{12x{x^{2}}^{(2x^{2})}*2ln(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 12x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 48{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 48x({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{48x{x^{2}}^{(2x^{2})}*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 48x{x^{2}}^{(2x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 8*3x^{2}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{8x^{3}{x^{2}}^{x^{2}}*3ln^{2}(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 8x^{3}{x^{2}}^{x^{2}}ln^{3}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 24*3x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{24x^{3}{x^{2}}^{x^{2}}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 24x^{3}{x^{2}}^{x^{2}}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{24x^{3}{x^{2}}^{(2x^{2})}*3ln^{2}(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 24x^{3}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 72*3x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{72x^{3}{x^{2}}^{(2x^{2})}*2ln(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 72x^{3}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 24*3x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{24x^{3}{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 24x^{3}{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 36{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 36x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 36x{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 72*3x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{72x^{3}{x^{2}}^{(2x^{2})}*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 72x^{3}{x^{2}}^{(2x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 36{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 36x({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))sin({x^{2}}^{x^{2}}) - 36x{x^{2}}^{(2x^{2})}cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 8*3x^{2}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 8x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - \frac{8x^{3}{x^{2}}^{(3x^{2})}*3ln^{2}(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} - 8x^{3}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - \frac{24x^{3}{x^{2}}^{(3x^{2})}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} - 24x^{3}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) - \frac{24x^{3}{x^{2}}^{(3x^{2})}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} - 24x^{3}{x^{2}}^{(3x^{2})}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 8*3x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 8x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))sin({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 8*3x^{2}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}}) - 8x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&12{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 48x^{2}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 240x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 104{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) - 144x^{2}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 720x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 336x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 140{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 1008x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{4{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x^{2}} - 104{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 140{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 12{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 48x^{2}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 240x^{2}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 336x^{2}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{x^{2}}ln^{4}(x^{2})cos({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 112x^{4}{x^{2}}^{(2x^{2})}ln^{4}(x^{2})sin({x^{2}}^{x^{2}}) - 448x^{4}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) + 96x^{4}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 672x^{4}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 96x^{4}{x^{2}}^{(3x^{2})}ln^{4}(x^{2})cos({x^{2}}^{x^{2}}) - 384x^{4}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 576x^{4}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 144x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 448x^{4}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 432x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 384x^{4}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) - 144x^{2}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{(4x^{2})}ln^{4}(x^{2})sin({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{(4x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) + 96x^{4}{x^{2}}^{(4x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{(4x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 112x^{4}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 96x^{4}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{(4x^{2})}sin({x^{2}}^{x^{2}})\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sin({({x}^{2})}^{{x}^{2}}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin({x^{2}}^{x^{2}})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin({x^{2}}^{x^{2}})\right)}{dx}\\=&cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&2x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 2x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 2x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})\right)}{dx}\\=&2{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 2x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{2x{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 2x{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 2{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 2x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 2x{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&2{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 6{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 8x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}})\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 6{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 8x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}})\right)}{dx}\\=&2({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{2{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 2{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 4*2x{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 4x^{2}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{4x^{2}{x^{2}}^{x^{2}}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 4x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 8*2x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{2}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{8x^{2}{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 8x^{2}{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 6({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 6{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 4*2x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 4x^{2}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{4x^{2}{x^{2}}^{(2x^{2})}*2ln(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 4x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 8*2x{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 8x^{2}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{8x^{2}{x^{2}}^{(2x^{2})}*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 8x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 4*2x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 4x^{2}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 4x^{2}{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 4*2x{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 4x^{2}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))sin({x^{2}}^{x^{2}}) - 4x^{2}{x^{2}}^{(2x^{2})}cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&12x{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 48x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{4{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x} - 12x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 48x{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 36x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 36x{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}})\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 12x{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 48x{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{4{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x} - 12x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 48x{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 24x^{3}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 36x{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 72x^{3}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 36x{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}})\right)}{dx}\\=&12{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 12x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{12x{x^{2}}^{x^{2}}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 12x{x^{2}}^{x^{2}}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 48{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 48x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{48x{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 48x{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + \frac{4*-{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x^{2}} + \frac{4({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}})}{x} + \frac{4{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))}{x} - 12{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 12x({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{12x{x^{2}}^{(2x^{2})}*2ln(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 12x{x^{2}}^{(2x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 48{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 48x({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{48x{x^{2}}^{(2x^{2})}*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 48x{x^{2}}^{(2x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 8*3x^{2}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 8x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{8x^{3}{x^{2}}^{x^{2}}*3ln^{2}(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 8x^{3}{x^{2}}^{x^{2}}ln^{3}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 24*3x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + \frac{24x^{3}{x^{2}}^{x^{2}}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 24x^{3}{x^{2}}^{x^{2}}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{24x^{3}{x^{2}}^{(2x^{2})}*3ln^{2}(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 24x^{3}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 72*3x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - \frac{72x^{3}{x^{2}}^{(2x^{2})}*2ln(x^{2})*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 72x^{3}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 24*3x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 24x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) + \frac{24x^{3}{x^{2}}^{x^{2}}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} + 24x^{3}{x^{2}}^{x^{2}}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 36{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 36x({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 36x{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 72*3x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 72x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{72x^{3}{x^{2}}^{(2x^{2})}*2xsin({x^{2}}^{x^{2}})}{(x^{2})} - 72x^{3}{x^{2}}^{(2x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 36{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 36x({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))sin({x^{2}}^{x^{2}}) - 36x{x^{2}}^{(2x^{2})}cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 8*3x^{2}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 8x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - \frac{8x^{3}{x^{2}}^{(3x^{2})}*3ln^{2}(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} - 8x^{3}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - \frac{24x^{3}{x^{2}}^{(3x^{2})}*2ln(x^{2})*2xcos({x^{2}}^{x^{2}})}{(x^{2})} - 24x^{3}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))ln(x^{2})cos({x^{2}}^{x^{2}}) - \frac{24x^{3}{x^{2}}^{(3x^{2})}*2xcos({x^{2}}^{x^{2}})}{(x^{2})} - 24x^{3}{x^{2}}^{(3x^{2})}ln(x^{2})*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) + 8*3x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) + 8x^{3}({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) + 8x^{3}{x^{2}}^{x^{2}}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 24*3x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 24x^{3}({x^{2}}^{(2x^{2})}((2*2x)ln(x^{2}) + \frac{(2x^{2})(2x)}{(x^{2})}))sin({x^{2}}^{x^{2}}) - 24x^{3}{x^{2}}^{(2x^{2})}cos({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})})) - 8*3x^{2}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}}) - 8x^{3}({x^{2}}^{(3x^{2})}((3*2x)ln(x^{2}) + \frac{(3x^{2})(2x)}{(x^{2})}))cos({x^{2}}^{x^{2}}) - 8x^{3}{x^{2}}^{(3x^{2})}*-sin({x^{2}}^{x^{2}})({x^{2}}^{x^{2}}((2x)ln(x^{2}) + \frac{(x^{2})(2x)}{(x^{2})}))\\=&12{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 48x^{2}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) + 240x^{2}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 104{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) - 144x^{2}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) - 720x^{2}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 336x^{2}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 140{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 1008x^{2}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - \frac{4{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}})}{x^{2}} - 104{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 140{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 12{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 48x^{2}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 240x^{2}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 336x^{2}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{x^{2}}ln^{4}(x^{2})cos({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{x^{2}}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 112x^{4}{x^{2}}^{(2x^{2})}ln^{4}(x^{2})sin({x^{2}}^{x^{2}}) - 448x^{4}{x^{2}}^{(2x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) + 96x^{4}{x^{2}}^{x^{2}}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) - 672x^{4}{x^{2}}^{(2x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) - 96x^{4}{x^{2}}^{(3x^{2})}ln^{4}(x^{2})cos({x^{2}}^{x^{2}}) - 384x^{4}{x^{2}}^{(3x^{2})}ln^{3}(x^{2})cos({x^{2}}^{x^{2}}) - 576x^{4}{x^{2}}^{(3x^{2})}ln^{2}(x^{2})cos({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{x^{2}}ln(x^{2})cos({x^{2}}^{x^{2}}) + 144x^{2}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 448x^{4}{x^{2}}^{(2x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) - 432x^{2}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 384x^{4}{x^{2}}^{(3x^{2})}ln(x^{2})cos({x^{2}}^{x^{2}}) - 144x^{2}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{(4x^{2})}ln^{4}(x^{2})sin({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{(4x^{2})}ln^{3}(x^{2})sin({x^{2}}^{x^{2}}) + 96x^{4}{x^{2}}^{(4x^{2})}ln^{2}(x^{2})sin({x^{2}}^{x^{2}}) + 64x^{4}{x^{2}}^{(4x^{2})}ln(x^{2})sin({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{x^{2}}cos({x^{2}}^{x^{2}}) - 112x^{4}{x^{2}}^{(2x^{2})}sin({x^{2}}^{x^{2}}) - 96x^{4}{x^{2}}^{(3x^{2})}cos({x^{2}}^{x^{2}}) + 16x^{4}{x^{2}}^{(4x^{2})}sin({x^{2}}^{x^{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。