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 8 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数e^{sin({x}^{2})} 关于 x 的 8 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = e^{sin(x^{2})}\\\\ &\color{blue}{函数的 8 阶导数：} \\=&1680e^{sin(x^{2})}cos^{4}(x^{2}) + 13440x^{2}e^{sin(x^{2})}cos^{5}(x^{2}) - 134400x^{2}e^{sin(x^{2})}sin(x^{2})cos^{3}(x^{2}) - 10080e^{sin(x^{2})}sin(x^{2})cos^{2}(x^{2}) - 201600x^{4}e^{sin(x^{2})}sin(x^{2})cos^{4}(x^{2}) - 134400x^{2}e^{sin(x^{2})}cos^{3}(x^{2}) + 201600x^{2}e^{sin(x^{2})}sin^{2}(x^{2})cos(x^{2}) + 13440x^{4}e^{sin(x^{2})}cos^{6}(x^{2}) - 7168x^{8}e^{sin(x^{2})}sin(x^{2})cos^{6}(x^{2}) + 604800x^{4}e^{sin(x^{2})}sin^{2}(x^{2})cos^{2}(x^{2}) - 268800x^{4}e^{sin(x^{2})}cos^{4}(x^{2}) - 75264x^{6}e^{sin(x^{2})}sin(x^{2})cos^{5}(x^{2}) + 1008000x^{4}e^{sin(x^{2})}sin(x^{2})cos^{2}(x^{2}) - 14336x^{8}e^{sin(x^{2})}cos^{6}(x^{2}) + 53760x^{8}e^{sin(x^{2})}sin^{2}(x^{2})cos^{4}(x^{2}) + 161280x^{8}e^{sin(x^{2})}sin(x^{2})cos^{4}(x^{2}) + 376320x^{6}e^{sin(x^{2})}sin^{2}(x^{2})cos^{3}(x^{2}) - 6720e^{sin(x^{2})}cos^{2}(x^{2}) - 125440x^{6}e^{sin(x^{2})}cos^{5}(x^{2}) - 107520x^{8}e^{sin(x^{2})}sin^{3}(x^{2})cos^{2}(x^{2}) + 878080x^{6}e^{sin(x^{2})}sin(x^{2})cos^{3}(x^{2}) - 322560x^{8}e^{sin(x^{2})}sin^{2}(x^{2})cos^{2}(x^{2}) + 86016x^{8}e^{sin(x^{2})}cos^{4}(x^{2}) - 376320x^{6}e^{sin(x^{2})}sin^{3}(x^{2})cos(x^{2}) - 752640x^{6}e^{sin(x^{2})}sin^{2}(x^{2})cos(x^{2}) - 193536x^{8}e^{sin(x^{2})}sin(x^{2})cos^{2}(x^{2}) + 201600x^{2}e^{sin(x^{2})}sin(x^{2})cos(x^{2}) + 326144x^{6}e^{sin(x^{2})}cos^{3}(x^{2}) - 225792x^{6}e^{sin(x^{2})}sin(x^{2})cos(x^{2}) + 3584x^{6}e^{sin(x^{2})}cos^{7}(x^{2}) + 26880x^{8}e^{sin(x^{2})}sin^{4}(x^{2}) + 215040x^{4}e^{sin(x^{2})}cos^{2}(x^{2}) - 201600x^{4}e^{sin(x^{2})}sin^{2}(x^{2}) + 53760x^{8}e^{sin(x^{2})}sin^{3}(x^{2}) - 201600x^{4}e^{sin(x^{2})}sin^{3}(x^{2}) - 16384x^{8}e^{sin(x^{2})}cos^{2}(x^{2}) + 16128x^{8}e^{sin(x^{2})}sin^{2}(x^{2}) + 5040e^{sin(x^{2})}sin^{2}(x^{2}) + 256x^{8}e^{sin(x^{2})}cos^{8}(x^{2}) + 1680e^{sin(x^{2})}sin(x^{2}) + 13440x^{2}e^{sin(x^{2})}cos(x^{2}) - 13440x^{4}e^{sin(x^{2})}sin(x^{2}) - 3584x^{6}e^{sin(x^{2})}cos(x^{2}) + 256x^{8}e^{sin(x^{2})}sin(x^{2})\\ \end{split}\end{equation} \]
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