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。
\[ \begin{equation}\begin{split}【1/1】求函数e^{e^{sin(x)}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{e^{sin(x)}}\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( e^{e^{sin(x)}}e^{sin(x)}cos(x)\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}cos(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)cos(x) + e^{e^{sin(x)}}e^{sin(x)}*-sin(x)\\=&e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{2}(x) - e^{e^{sin(x)}}e^{sin(x)}sin(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{2}(x) - e^{e^{sin(x)}}e^{sin(x)}sin(x)\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{2}}cos^{2}(x) + e^{e^{sin(x)}}*2e^{sin(x)}e^{sin(x)}cos(x)cos^{2}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}*-2cos(x)sin(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}*-2cos(x)sin(x) - e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}sin(x) - e^{e^{sin(x)}}e^{sin(x)}cos(x)sin(x) - e^{e^{sin(x)}}e^{sin(x)}cos(x)\\=&e^{e^{sin(x)}}e^{{sin(x)}*{3}}cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{3}(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)cos(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{3}(x) - 3e^{e^{sin(x)}}e^{sin(x)}sin(x)cos(x) - e^{sin(x)}e^{e^{sin(x)}}cos(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( e^{e^{sin(x)}}e^{{sin(x)}*{3}}cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{3}(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)cos(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{3}(x) - 3e^{e^{sin(x)}}e^{sin(x)}sin(x)cos(x) - e^{sin(x)}e^{e^{sin(x)}}cos(x)\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{3}}cos^{3}(x) + e^{e^{sin(x)}}*3e^{{sin(x)}*{2}}e^{sin(x)}cos(x)cos^{3}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{3}}*-3cos^{2}(x)sin(x) + 2*2e^{sin(x)}e^{sin(x)}cos(x)e^{e^{sin(x)}}cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}e^{sin(x)}cos(x)cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}*-3cos^{2}(x)sin(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{2}}sin(x)cos(x) - 3e^{e^{sin(x)}}*2e^{sin(x)}e^{sin(x)}cos(x)sin(x)cos(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos(x)cos(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)*-sin(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{2}}cos^{3}(x) + e^{e^{sin(x)}}*2e^{sin(x)}e^{sin(x)}cos(x)cos^{3}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}*-3cos^{2}(x)sin(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}*-3cos^{2}(x)sin(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}sin(x)cos(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)sin(x)cos(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)cos(x) - 3e^{e^{sin(x)}}e^{sin(x)}sin(x)*-sin(x) - e^{sin(x)}cos(x)e^{e^{sin(x)}}cos(x) - e^{sin(x)}e^{e^{sin(x)}}e^{sin(x)}cos(x)cos(x) - e^{sin(x)}e^{e^{sin(x)}}*-sin(x)\\=&e^{e^{sin(x)}}e^{{sin(x)}*{4}}cos^{4}(x) + 5e^{{sin(x)}*{3}}e^{e^{sin(x)}}cos^{4}(x) - 6e^{e^{sin(x)}}e^{sin(x)}sin(x)cos^{2}(x) + 6e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{4}(x) - 12e^{{sin(x)}*{2}}e^{e^{sin(x)}}sin(x)cos^{2}(x) - 6e^{e^{sin(x)}}e^{{sin(x)}*{3}}sin(x)cos^{2}(x) - 4e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{2}(x) - 6e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)cos^{2}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{3}}cos^{4}(x) + 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin^{2}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{4}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{4}(x) - 4e^{sin(x)}e^{e^{sin(x)}}cos^{2}(x) + 3e^{e^{sin(x)}}e^{sin(x)}sin^{2}(x) + e^{sin(x)}e^{e^{sin(x)}}sin(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数e^{e^{sin(x)}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{e^{sin(x)}}\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( e^{e^{sin(x)}}e^{sin(x)}cos(x)\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}cos(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)cos(x) + e^{e^{sin(x)}}e^{sin(x)}*-sin(x)\\=&e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{2}(x) - e^{e^{sin(x)}}e^{sin(x)}sin(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{2}(x) - e^{e^{sin(x)}}e^{sin(x)}sin(x)\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{2}}cos^{2}(x) + e^{e^{sin(x)}}*2e^{sin(x)}e^{sin(x)}cos(x)cos^{2}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}*-2cos(x)sin(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)cos^{2}(x) + e^{e^{sin(x)}}e^{sin(x)}*-2cos(x)sin(x) - e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}sin(x) - e^{e^{sin(x)}}e^{sin(x)}cos(x)sin(x) - e^{e^{sin(x)}}e^{sin(x)}cos(x)\\=&e^{e^{sin(x)}}e^{{sin(x)}*{3}}cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{3}(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)cos(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{3}(x) - 3e^{e^{sin(x)}}e^{sin(x)}sin(x)cos(x) - e^{sin(x)}e^{e^{sin(x)}}cos(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( e^{e^{sin(x)}}e^{{sin(x)}*{3}}cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{3}(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)cos(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{3}(x) - 3e^{e^{sin(x)}}e^{sin(x)}sin(x)cos(x) - e^{sin(x)}e^{e^{sin(x)}}cos(x)\right)}{dx}\\=&e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{3}}cos^{3}(x) + e^{e^{sin(x)}}*3e^{{sin(x)}*{2}}e^{sin(x)}cos(x)cos^{3}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{3}}*-3cos^{2}(x)sin(x) + 2*2e^{sin(x)}e^{sin(x)}cos(x)e^{e^{sin(x)}}cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}e^{sin(x)}cos(x)cos^{3}(x) + 2e^{{sin(x)}*{2}}e^{e^{sin(x)}}*-3cos^{2}(x)sin(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{2}}sin(x)cos(x) - 3e^{e^{sin(x)}}*2e^{sin(x)}e^{sin(x)}cos(x)sin(x)cos(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos(x)cos(x) - 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)*-sin(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{{sin(x)}*{2}}cos^{3}(x) + e^{e^{sin(x)}}*2e^{sin(x)}e^{sin(x)}cos(x)cos^{3}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}*-3cos^{2}(x)sin(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}cos(x)cos^{3}(x) + e^{e^{sin(x)}}e^{sin(x)}*-3cos^{2}(x)sin(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)e^{sin(x)}sin(x)cos(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)sin(x)cos(x) - 3e^{e^{sin(x)}}e^{sin(x)}cos(x)cos(x) - 3e^{e^{sin(x)}}e^{sin(x)}sin(x)*-sin(x) - e^{sin(x)}cos(x)e^{e^{sin(x)}}cos(x) - e^{sin(x)}e^{e^{sin(x)}}e^{sin(x)}cos(x)cos(x) - e^{sin(x)}e^{e^{sin(x)}}*-sin(x)\\=&e^{e^{sin(x)}}e^{{sin(x)}*{4}}cos^{4}(x) + 5e^{{sin(x)}*{3}}e^{e^{sin(x)}}cos^{4}(x) - 6e^{e^{sin(x)}}e^{sin(x)}sin(x)cos^{2}(x) + 6e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{4}(x) - 12e^{{sin(x)}*{2}}e^{e^{sin(x)}}sin(x)cos^{2}(x) - 6e^{e^{sin(x)}}e^{{sin(x)}*{3}}sin(x)cos^{2}(x) - 4e^{{sin(x)}*{2}}e^{e^{sin(x)}}cos^{2}(x) - 6e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin(x)cos^{2}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{3}}cos^{4}(x) + 3e^{e^{sin(x)}}e^{{sin(x)}*{2}}sin^{2}(x) + e^{e^{sin(x)}}e^{{sin(x)}*{2}}cos^{4}(x) + e^{e^{sin(x)}}e^{sin(x)}cos^{4}(x) - 4e^{sin(x)}e^{e^{sin(x)}}cos^{2}(x) + 3e^{e^{sin(x)}}e^{sin(x)}sin^{2}(x) + e^{sin(x)}e^{e^{sin(x)}}sin(x)\\ \end{split}\end{equation} \]
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