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。
\[ \begin{equation}\begin{split}【1/1】求函数{e}^{sin({x}^{2})} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {e}^{sin(x^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {e}^{sin(x^{2})}\right)}{dx}\\=&({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))\\=&2x{e}^{sin(x^{2})}cos(x^{2})\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2x{e}^{sin(x^{2})}cos(x^{2})\right)}{dx}\\=&2{e}^{sin(x^{2})}cos(x^{2}) + 2x({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))cos(x^{2}) + 2x{e}^{sin(x^{2})}*-sin(x^{2})*2x\\=&2{e}^{sin(x^{2})}cos(x^{2}) + 4x^{2}{e}^{sin(x^{2})}cos^{2}(x^{2}) - 4x^{2}{e}^{sin(x^{2})}sin(x^{2})\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2{e}^{sin(x^{2})}cos(x^{2}) + 4x^{2}{e}^{sin(x^{2})}cos^{2}(x^{2}) - 4x^{2}{e}^{sin(x^{2})}sin(x^{2})\right)}{dx}\\=&2({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))cos(x^{2}) + 2{e}^{sin(x^{2})}*-sin(x^{2})*2x + 4*2x{e}^{sin(x^{2})}cos^{2}(x^{2}) + 4x^{2}({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))cos^{2}(x^{2}) + 4x^{2}{e}^{sin(x^{2})}*-2cos(x^{2})sin(x^{2})*2x - 4*2x{e}^{sin(x^{2})}sin(x^{2}) - 4x^{2}({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))sin(x^{2}) - 4x^{2}{e}^{sin(x^{2})}cos(x^{2})*2x\\=&12x{e}^{sin(x^{2})}cos^{2}(x^{2}) - 24x^{3}{e}^{sin(x^{2})}sin(x^{2})cos(x^{2}) + 8x^{3}{e}^{sin(x^{2})}cos^{3}(x^{2}) - 12x{e}^{sin(x^{2})}sin(x^{2}) - 8x^{3}{e}^{sin(x^{2})}cos(x^{2})\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 12x{e}^{sin(x^{2})}cos^{2}(x^{2}) - 24x^{3}{e}^{sin(x^{2})}sin(x^{2})cos(x^{2}) + 8x^{3}{e}^{sin(x^{2})}cos^{3}(x^{2}) - 12x{e}^{sin(x^{2})}sin(x^{2}) - 8x^{3}{e}^{sin(x^{2})}cos(x^{2})\right)}{dx}\\=&12{e}^{sin(x^{2})}cos^{2}(x^{2}) + 12x({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))cos^{2}(x^{2}) + 12x{e}^{sin(x^{2})}*-2cos(x^{2})sin(x^{2})*2x - 24*3x^{2}{e}^{sin(x^{2})}sin(x^{2})cos(x^{2}) - 24x^{3}({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))sin(x^{2})cos(x^{2}) - 24x^{3}{e}^{sin(x^{2})}cos(x^{2})*2xcos(x^{2}) - 24x^{3}{e}^{sin(x^{2})}sin(x^{2})*-sin(x^{2})*2x + 8*3x^{2}{e}^{sin(x^{2})}cos^{3}(x^{2}) + 8x^{3}({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))cos^{3}(x^{2}) + 8x^{3}{e}^{sin(x^{2})}*-3cos^{2}(x^{2})sin(x^{2})*2x - 12{e}^{sin(x^{2})}sin(x^{2}) - 12x({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))sin(x^{2}) - 12x{e}^{sin(x^{2})}cos(x^{2})*2x - 8*3x^{2}{e}^{sin(x^{2})}cos(x^{2}) - 8x^{3}({e}^{sin(x^{2})}((cos(x^{2})*2x)ln(e) + \frac{(sin(x^{2}))(0)}{(e)}))cos(x^{2}) - 8x^{3}{e}^{sin(x^{2})}*-sin(x^{2})*2x\\=&12{e}^{sin(x^{2})}cos^{2}(x^{2}) + 48x^{2}{e}^{sin(x^{2})}cos^{3}(x^{2}) - 144x^{2}{e}^{sin(x^{2})}sin(x^{2})cos(x^{2}) - 96x^{4}{e}^{sin(x^{2})}sin(x^{2})cos^{2}(x^{2}) - 64x^{4}{e}^{sin(x^{2})}cos^{2}(x^{2}) + 16x^{4}{e}^{sin(x^{2})}cos^{4}(x^{2}) + 48x^{4}{e}^{sin(x^{2})}sin^{2}(x^{2}) - 12{e}^{sin(x^{2})}sin(x^{2}) - 48x^{2}{e}^{sin(x^{2})}cos(x^{2}) + 16x^{4}{e}^{sin(x^{2})}sin(x^{2})\\ \end{split}\end{equation} \]
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