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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{{e}^{x}}{cos(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{{e}^{x}}{cos(x)}\right)}{dx}\\=&\frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{cos(x)} + \frac{{e}^{x}sin(x)}{cos^{2}(x)}\\=&\frac{{e}^{x}}{cos(x)} + \frac{{e}^{x}sin(x)}{cos^{2}(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{e}^{x}}{cos(x)} + \frac{{e}^{x}sin(x)}{cos^{2}(x)}\right)}{dx}\\=&\frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{cos(x)} + \frac{{e}^{x}sin(x)}{cos^{2}(x)} + \frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)}{cos^{2}(x)} + \frac{{e}^{x}cos(x)}{cos^{2}(x)} + \frac{{e}^{x}sin(x)*2sin(x)}{cos^{3}(x)}\\=&\frac{2{e}^{x}}{cos(x)} + \frac{2{e}^{x}sin(x)}{cos^{2}(x)} + \frac{2{e}^{x}sin^{2}(x)}{cos^{3}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2{e}^{x}}{cos(x)} + \frac{2{e}^{x}sin(x)}{cos^{2}(x)} + \frac{2{e}^{x}sin^{2}(x)}{cos^{3}(x)}\right)}{dx}\\=&\frac{2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{cos(x)} + \frac{2{e}^{x}sin(x)}{cos^{2}(x)} + \frac{2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)}{cos^{2}(x)} + \frac{2{e}^{x}cos(x)}{cos^{2}(x)} + \frac{2{e}^{x}sin(x)*2sin(x)}{cos^{3}(x)} + \frac{2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)}{cos^{3}(x)} + \frac{2{e}^{x}*2sin(x)cos(x)}{cos^{3}(x)} + \frac{2{e}^{x}sin^{2}(x)*3sin(x)}{cos^{4}(x)}\\=&\frac{4{e}^{x}}{cos(x)} + \frac{8{e}^{x}sin(x)}{cos^{2}(x)} + \frac{6{e}^{x}sin^{2}(x)}{cos^{3}(x)} + \frac{6{e}^{x}sin^{3}(x)}{cos^{4}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{4{e}^{x}}{cos(x)} + \frac{8{e}^{x}sin(x)}{cos^{2}(x)} + \frac{6{e}^{x}sin^{2}(x)}{cos^{3}(x)} + \frac{6{e}^{x}sin^{3}(x)}{cos^{4}(x)}\right)}{dx}\\=&\frac{4({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{cos(x)} + \frac{4{e}^{x}sin(x)}{cos^{2}(x)} + \frac{8({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)}{cos^{2}(x)} + \frac{8{e}^{x}cos(x)}{cos^{2}(x)} + \frac{8{e}^{x}sin(x)*2sin(x)}{cos^{3}(x)} + \frac{6({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)}{cos^{3}(x)} + \frac{6{e}^{x}*2sin(x)cos(x)}{cos^{3}(x)} + \frac{6{e}^{x}sin^{2}(x)*3sin(x)}{cos^{4}(x)} + \frac{6({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{3}(x)}{cos^{4}(x)} + \frac{6{e}^{x}*3sin^{2}(x)cos(x)}{cos^{4}(x)} + \frac{6{e}^{x}sin^{3}(x)*4sin(x)}{cos^{5}(x)}\\=&\frac{12{e}^{x}}{cos(x)} + \frac{24{e}^{x}sin(x)}{cos^{2}(x)} + \frac{40{e}^{x}sin^{2}(x)}{cos^{3}(x)} + \frac{24{e}^{x}sin^{3}(x)}{cos^{4}(x)} + \frac{24{e}^{x}sin^{4}(x)}{cos^{5}(x)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{{e}^{x}}{cos(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{{e}^{x}}{cos(x)}\right)}{dx}\\=&\frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{cos(x)} + \frac{{e}^{x}sin(x)}{cos^{2}(x)}\\=&\frac{{e}^{x}}{cos(x)} + \frac{{e}^{x}sin(x)}{cos^{2}(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{e}^{x}}{cos(x)} + \frac{{e}^{x}sin(x)}{cos^{2}(x)}\right)}{dx}\\=&\frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{cos(x)} + \frac{{e}^{x}sin(x)}{cos^{2}(x)} + \frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)}{cos^{2}(x)} + \frac{{e}^{x}cos(x)}{cos^{2}(x)} + \frac{{e}^{x}sin(x)*2sin(x)}{cos^{3}(x)}\\=&\frac{2{e}^{x}}{cos(x)} + \frac{2{e}^{x}sin(x)}{cos^{2}(x)} + \frac{2{e}^{x}sin^{2}(x)}{cos^{3}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2{e}^{x}}{cos(x)} + \frac{2{e}^{x}sin(x)}{cos^{2}(x)} + \frac{2{e}^{x}sin^{2}(x)}{cos^{3}(x)}\right)}{dx}\\=&\frac{2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{cos(x)} + \frac{2{e}^{x}sin(x)}{cos^{2}(x)} + \frac{2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)}{cos^{2}(x)} + \frac{2{e}^{x}cos(x)}{cos^{2}(x)} + \frac{2{e}^{x}sin(x)*2sin(x)}{cos^{3}(x)} + \frac{2({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)}{cos^{3}(x)} + \frac{2{e}^{x}*2sin(x)cos(x)}{cos^{3}(x)} + \frac{2{e}^{x}sin^{2}(x)*3sin(x)}{cos^{4}(x)}\\=&\frac{4{e}^{x}}{cos(x)} + \frac{8{e}^{x}sin(x)}{cos^{2}(x)} + \frac{6{e}^{x}sin^{2}(x)}{cos^{3}(x)} + \frac{6{e}^{x}sin^{3}(x)}{cos^{4}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{4{e}^{x}}{cos(x)} + \frac{8{e}^{x}sin(x)}{cos^{2}(x)} + \frac{6{e}^{x}sin^{2}(x)}{cos^{3}(x)} + \frac{6{e}^{x}sin^{3}(x)}{cos^{4}(x)}\right)}{dx}\\=&\frac{4({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{cos(x)} + \frac{4{e}^{x}sin(x)}{cos^{2}(x)} + \frac{8({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)}{cos^{2}(x)} + \frac{8{e}^{x}cos(x)}{cos^{2}(x)} + \frac{8{e}^{x}sin(x)*2sin(x)}{cos^{3}(x)} + \frac{6({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)}{cos^{3}(x)} + \frac{6{e}^{x}*2sin(x)cos(x)}{cos^{3}(x)} + \frac{6{e}^{x}sin^{2}(x)*3sin(x)}{cos^{4}(x)} + \frac{6({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{3}(x)}{cos^{4}(x)} + \frac{6{e}^{x}*3sin^{2}(x)cos(x)}{cos^{4}(x)} + \frac{6{e}^{x}sin^{3}(x)*4sin(x)}{cos^{5}(x)}\\=&\frac{12{e}^{x}}{cos(x)} + \frac{24{e}^{x}sin(x)}{cos^{2}(x)} + \frac{40{e}^{x}sin^{2}(x)}{cos^{3}(x)} + \frac{24{e}^{x}sin^{3}(x)}{cos^{4}(x)} + \frac{24{e}^{x}sin^{4}(x)}{cos^{5}(x)}\\ \end{split}\end{equation} \]
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