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} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!