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 3 个题目：每一题对 x 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/3】求函数e^{sin(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{sin(x)}\right)}{dx}\\=&e^{sin(x)}cos(x)\\=&e^{sin(x)}cos(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( e^{sin(x)}cos(x)\right)}{dx}\\=&e^{sin(x)}cos(x)cos(x) + e^{sin(x)}*-sin(x)\\=&e^{sin(x)}cos^{2}(x) - e^{sin(x)}sin(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{sin(x)}cos^{2}(x) - e^{sin(x)}sin(x)\right)}{dx}\\=&e^{sin(x)}cos(x)cos^{2}(x) + e^{sin(x)}*-2cos(x)sin(x) - e^{sin(x)}cos(x)sin(x) - e^{sin(x)}cos(x)\\=&e^{sin(x)}cos^{3}(x) - 3e^{sin(x)}sin(x)cos(x) - e^{sin(x)}cos(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( e^{sin(x)}cos^{3}(x) - 3e^{sin(x)}sin(x)cos(x) - e^{sin(x)}cos(x)\right)}{dx}\\=&e^{sin(x)}cos(x)cos^{3}(x) + e^{sin(x)}*-3cos^{2}(x)sin(x) - 3e^{sin(x)}cos(x)sin(x)cos(x) - 3e^{sin(x)}cos(x)cos(x) - 3e^{sin(x)}sin(x)*-sin(x) - e^{sin(x)}cos(x)cos(x) - e^{sin(x)}*-sin(x)\\=&e^{sin(x)}cos^{4}(x) - 6e^{sin(x)}sin(x)cos^{2}(x) - 4e^{sin(x)}cos^{2}(x) + 3e^{sin(x)}sin^{2}(x) + e^{sin(x)}sin(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/3】求函数e^{cos(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{cos(x)}\right)}{dx}\\=&e^{cos(x)}*-sin(x)\\=&-e^{cos(x)}sin(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -e^{cos(x)}sin(x)\right)}{dx}\\=&-e^{cos(x)}*-sin(x)sin(x) - e^{cos(x)}cos(x)\\=&e^{cos(x)}sin^{2}(x) - e^{cos(x)}cos(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{cos(x)}sin^{2}(x) - e^{cos(x)}cos(x)\right)}{dx}\\=&e^{cos(x)}*-sin(x)sin^{2}(x) + e^{cos(x)}*2sin(x)cos(x) - e^{cos(x)}*-sin(x)cos(x) - e^{cos(x)}*-sin(x)\\=&3e^{cos(x)}sin(x)cos(x) - e^{cos(x)}sin^{3}(x) + e^{cos(x)}sin(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 3e^{cos(x)}sin(x)cos(x) - e^{cos(x)}sin^{3}(x) + e^{cos(x)}sin(x)\right)}{dx}\\=&3e^{cos(x)}*-sin(x)sin(x)cos(x) + 3e^{cos(x)}cos(x)cos(x) + 3e^{cos(x)}sin(x)*-sin(x) - e^{cos(x)}*-sin(x)sin^{3}(x) - e^{cos(x)}*3sin^{2}(x)cos(x) + e^{cos(x)}*-sin(x)sin(x) + e^{cos(x)}cos(x)\\=&-6e^{cos(x)}sin^{2}(x)cos(x) + 3e^{cos(x)}cos^{2}(x) - 4e^{cos(x)}sin^{2}(x) + e^{cos(x)}sin^{4}(x) + e^{cos(x)}cos(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【3/3】求函数e^{tan(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{tan(x)}\right)}{dx}\\=&e^{tan(x)}sec^{2}(x)(1)\\=&e^{tan(x)}sec^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( e^{tan(x)}sec^{2}(x)\right)}{dx}\\=&e^{tan(x)}sec^{2}(x)(1)sec^{2}(x) + e^{tan(x)}*2sec^{2}(x)tan(x)\\=&e^{tan(x)}sec^{4}(x) + 2e^{tan(x)}tan(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{tan(x)}sec^{4}(x) + 2e^{tan(x)}tan(x)sec^{2}(x)\right)}{dx}\\=&e^{tan(x)}sec^{2}(x)(1)sec^{4}(x) + e^{tan(x)}*4sec^{4}(x)tan(x) + 2e^{tan(x)}sec^{2}(x)(1)tan(x)sec^{2}(x) + 2e^{tan(x)}sec^{2}(x)(1)sec^{2}(x) + 2e^{tan(x)}tan(x)*2sec^{2}(x)tan(x)\\=&e^{tan(x)}sec^{6}(x) + 6e^{tan(x)}tan(x)sec^{4}(x) + 2e^{tan(x)}sec^{4}(x) + 4e^{tan(x)}tan^{2}(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( e^{tan(x)}sec^{6}(x) + 6e^{tan(x)}tan(x)sec^{4}(x) + 2e^{tan(x)}sec^{4}(x) + 4e^{tan(x)}tan^{2}(x)sec^{2}(x)\right)}{dx}\\=&e^{tan(x)}sec^{2}(x)(1)sec^{6}(x) + e^{tan(x)}*6sec^{6}(x)tan(x) + 6e^{tan(x)}sec^{2}(x)(1)tan(x)sec^{4}(x) + 6e^{tan(x)}sec^{2}(x)(1)sec^{4}(x) + 6e^{tan(x)}tan(x)*4sec^{4}(x)tan(x) + 2e^{tan(x)}sec^{2}(x)(1)sec^{4}(x) + 2e^{tan(x)}*4sec^{4}(x)tan(x) + 4e^{tan(x)}sec^{2}(x)(1)tan^{2}(x)sec^{2}(x) + 4e^{tan(x)}*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 4e^{tan(x)}tan^{2}(x)*2sec^{2}(x)tan(x)\\=&e^{tan(x)}sec^{8}(x) + 12e^{tan(x)}tan(x)sec^{6}(x) + 28e^{tan(x)}tan^{2}(x)sec^{4}(x) + 8e^{tan(x)}sec^{6}(x) + 16e^{tan(x)}tan(x)sec^{4}(x) + 8e^{tan(x)}tan^{3}(x)sec^{2}(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/3】求函数e^{sin(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{sin(x)}\right)}{dx}\\=&e^{sin(x)}cos(x)\\=&e^{sin(x)}cos(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( e^{sin(x)}cos(x)\right)}{dx}\\=&e^{sin(x)}cos(x)cos(x) + e^{sin(x)}*-sin(x)\\=&e^{sin(x)}cos^{2}(x) - e^{sin(x)}sin(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{sin(x)}cos^{2}(x) - e^{sin(x)}sin(x)\right)}{dx}\\=&e^{sin(x)}cos(x)cos^{2}(x) + e^{sin(x)}*-2cos(x)sin(x) - e^{sin(x)}cos(x)sin(x) - e^{sin(x)}cos(x)\\=&e^{sin(x)}cos^{3}(x) - 3e^{sin(x)}sin(x)cos(x) - e^{sin(x)}cos(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( e^{sin(x)}cos^{3}(x) - 3e^{sin(x)}sin(x)cos(x) - e^{sin(x)}cos(x)\right)}{dx}\\=&e^{sin(x)}cos(x)cos^{3}(x) + e^{sin(x)}*-3cos^{2}(x)sin(x) - 3e^{sin(x)}cos(x)sin(x)cos(x) - 3e^{sin(x)}cos(x)cos(x) - 3e^{sin(x)}sin(x)*-sin(x) - e^{sin(x)}cos(x)cos(x) - e^{sin(x)}*-sin(x)\\=&e^{sin(x)}cos^{4}(x) - 6e^{sin(x)}sin(x)cos^{2}(x) - 4e^{sin(x)}cos^{2}(x) + 3e^{sin(x)}sin^{2}(x) + e^{sin(x)}sin(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/3】求函数e^{cos(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{cos(x)}\right)}{dx}\\=&e^{cos(x)}*-sin(x)\\=&-e^{cos(x)}sin(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -e^{cos(x)}sin(x)\right)}{dx}\\=&-e^{cos(x)}*-sin(x)sin(x) - e^{cos(x)}cos(x)\\=&e^{cos(x)}sin^{2}(x) - e^{cos(x)}cos(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{cos(x)}sin^{2}(x) - e^{cos(x)}cos(x)\right)}{dx}\\=&e^{cos(x)}*-sin(x)sin^{2}(x) + e^{cos(x)}*2sin(x)cos(x) - e^{cos(x)}*-sin(x)cos(x) - e^{cos(x)}*-sin(x)\\=&3e^{cos(x)}sin(x)cos(x) - e^{cos(x)}sin^{3}(x) + e^{cos(x)}sin(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 3e^{cos(x)}sin(x)cos(x) - e^{cos(x)}sin^{3}(x) + e^{cos(x)}sin(x)\right)}{dx}\\=&3e^{cos(x)}*-sin(x)sin(x)cos(x) + 3e^{cos(x)}cos(x)cos(x) + 3e^{cos(x)}sin(x)*-sin(x) - e^{cos(x)}*-sin(x)sin^{3}(x) - e^{cos(x)}*3sin^{2}(x)cos(x) + e^{cos(x)}*-sin(x)sin(x) + e^{cos(x)}cos(x)\\=&-6e^{cos(x)}sin^{2}(x)cos(x) + 3e^{cos(x)}cos^{2}(x) - 4e^{cos(x)}sin^{2}(x) + e^{cos(x)}sin^{4}(x) + e^{cos(x)}cos(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【3/3】求函数e^{tan(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{tan(x)}\right)}{dx}\\=&e^{tan(x)}sec^{2}(x)(1)\\=&e^{tan(x)}sec^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( e^{tan(x)}sec^{2}(x)\right)}{dx}\\=&e^{tan(x)}sec^{2}(x)(1)sec^{2}(x) + e^{tan(x)}*2sec^{2}(x)tan(x)\\=&e^{tan(x)}sec^{4}(x) + 2e^{tan(x)}tan(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( e^{tan(x)}sec^{4}(x) + 2e^{tan(x)}tan(x)sec^{2}(x)\right)}{dx}\\=&e^{tan(x)}sec^{2}(x)(1)sec^{4}(x) + e^{tan(x)}*4sec^{4}(x)tan(x) + 2e^{tan(x)}sec^{2}(x)(1)tan(x)sec^{2}(x) + 2e^{tan(x)}sec^{2}(x)(1)sec^{2}(x) + 2e^{tan(x)}tan(x)*2sec^{2}(x)tan(x)\\=&e^{tan(x)}sec^{6}(x) + 6e^{tan(x)}tan(x)sec^{4}(x) + 2e^{tan(x)}sec^{4}(x) + 4e^{tan(x)}tan^{2}(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( e^{tan(x)}sec^{6}(x) + 6e^{tan(x)}tan(x)sec^{4}(x) + 2e^{tan(x)}sec^{4}(x) + 4e^{tan(x)}tan^{2}(x)sec^{2}(x)\right)}{dx}\\=&e^{tan(x)}sec^{2}(x)(1)sec^{6}(x) + e^{tan(x)}*6sec^{6}(x)tan(x) + 6e^{tan(x)}sec^{2}(x)(1)tan(x)sec^{4}(x) + 6e^{tan(x)}sec^{2}(x)(1)sec^{4}(x) + 6e^{tan(x)}tan(x)*4sec^{4}(x)tan(x) + 2e^{tan(x)}sec^{2}(x)(1)sec^{4}(x) + 2e^{tan(x)}*4sec^{4}(x)tan(x) + 4e^{tan(x)}sec^{2}(x)(1)tan^{2}(x)sec^{2}(x) + 4e^{tan(x)}*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 4e^{tan(x)}tan^{2}(x)*2sec^{2}(x)tan(x)\\=&e^{tan(x)}sec^{8}(x) + 12e^{tan(x)}tan(x)sec^{6}(x) + 28e^{tan(x)}tan^{2}(x)sec^{4}(x) + 8e^{tan(x)}sec^{6}(x) + 16e^{tan(x)}tan(x)sec^{4}(x) + 8e^{tan(x)}tan^{3}(x)sec^{2}(x)\\ \end{split}\end{equation} \]
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