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。
\[ \begin{equation}\begin{split}【1/1】求函数sin(cos(ln(x))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(cos(ln(x)))\right)}{dx}\\=&\frac{cos(cos(ln(x)))*-sin(ln(x))}{(x)}\\=&\frac{-sin(ln(x))cos(cos(ln(x)))}{x}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-sin(ln(x))cos(cos(ln(x)))}{x}\right)}{dx}\\=&\frac{--sin(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{cos(ln(x))cos(cos(ln(x)))}{x(x)} - \frac{sin(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x(x)}\\=&\frac{sin(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{cos(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{sin(cos(ln(x)))sin^{2}(ln(x))}{x^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{sin(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{cos(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{sin(cos(ln(x)))sin^{2}(ln(x))}{x^{2}}\right)}{dx}\\=&\frac{-2sin(ln(x))cos(cos(ln(x)))}{x^{3}} + \frac{cos(ln(x))cos(cos(ln(x)))}{x^{2}(x)} + \frac{sin(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{2}(x)} - \frac{-2cos(ln(x))cos(cos(ln(x)))}{x^{3}} - \frac{-sin(ln(x))cos(cos(ln(x)))}{x^{2}(x)} - \frac{cos(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{2}(x)} - \frac{-2sin(cos(ln(x)))sin^{2}(ln(x))}{x^{3}} - \frac{cos(cos(ln(x)))*-sin(ln(x))sin^{2}(ln(x))}{x^{2}(x)} - \frac{sin(cos(ln(x)))*2sin(ln(x))cos(ln(x))}{x^{2}(x)}\\=&\frac{-sin(ln(x))cos(cos(ln(x)))}{x^{3}} + \frac{3cos(ln(x))cos(cos(ln(x)))}{x^{3}} - \frac{3sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{x^{3}} + \frac{3sin(cos(ln(x)))sin^{2}(ln(x))}{x^{3}} + \frac{sin^{3}(ln(x))cos(cos(ln(x)))}{x^{3}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-sin(ln(x))cos(cos(ln(x)))}{x^{3}} + \frac{3cos(ln(x))cos(cos(ln(x)))}{x^{3}} - \frac{3sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{x^{3}} + \frac{3sin(cos(ln(x)))sin^{2}(ln(x))}{x^{3}} + \frac{sin^{3}(ln(x))cos(cos(ln(x)))}{x^{3}}\right)}{dx}\\=&\frac{--3sin(ln(x))cos(cos(ln(x)))}{x^{4}} - \frac{cos(ln(x))cos(cos(ln(x)))}{x^{3}(x)} - \frac{sin(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{3}(x)} + \frac{3*-3cos(ln(x))cos(cos(ln(x)))}{x^{4}} + \frac{3*-sin(ln(x))cos(cos(ln(x)))}{x^{3}(x)} + \frac{3cos(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{3}(x)} - \frac{3*-3sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{x^{4}} - \frac{3cos(cos(ln(x)))*-sin(ln(x))sin(ln(x))cos(ln(x))}{x^{3}(x)} - \frac{3sin(cos(ln(x)))cos(ln(x))cos(ln(x))}{x^{3}(x)} - \frac{3sin(cos(ln(x)))sin(ln(x))*-sin(ln(x))}{x^{3}(x)} + \frac{3*-3sin(cos(ln(x)))sin^{2}(ln(x))}{x^{4}} + \frac{3cos(cos(ln(x)))*-sin(ln(x))sin^{2}(ln(x))}{x^{3}(x)} + \frac{3sin(cos(ln(x)))*2sin(ln(x))cos(ln(x))}{x^{3}(x)} + \frac{-3sin^{3}(ln(x))cos(cos(ln(x)))}{x^{4}} + \frac{3sin^{2}(ln(x))cos(ln(x))cos(cos(ln(x)))}{x^{3}(x)} + \frac{sin^{3}(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{3}(x)}\\=& - \frac{10cos(ln(x))cos(cos(ln(x)))}{x^{4}} + \frac{18sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{x^{4}} + \frac{3sin^{2}(ln(x))cos(ln(x))cos(cos(ln(x)))}{x^{4}} - \frac{7sin(cos(ln(x)))sin^{2}(ln(x))}{x^{4}} + \frac{3sin^{2}(ln(x))cos(cos(ln(x)))cos(ln(x))}{x^{4}} - \frac{3sin(cos(ln(x)))cos^{2}(ln(x))}{x^{4}} - \frac{6sin^{3}(ln(x))cos(cos(ln(x)))}{x^{4}} + \frac{sin(cos(ln(x)))sin^{4}(ln(x))}{x^{4}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sin(cos(ln(x))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(cos(ln(x)))\right)}{dx}\\=&\frac{cos(cos(ln(x)))*-sin(ln(x))}{(x)}\\=&\frac{-sin(ln(x))cos(cos(ln(x)))}{x}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-sin(ln(x))cos(cos(ln(x)))}{x}\right)}{dx}\\=&\frac{--sin(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{cos(ln(x))cos(cos(ln(x)))}{x(x)} - \frac{sin(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x(x)}\\=&\frac{sin(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{cos(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{sin(cos(ln(x)))sin^{2}(ln(x))}{x^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{sin(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{cos(ln(x))cos(cos(ln(x)))}{x^{2}} - \frac{sin(cos(ln(x)))sin^{2}(ln(x))}{x^{2}}\right)}{dx}\\=&\frac{-2sin(ln(x))cos(cos(ln(x)))}{x^{3}} + \frac{cos(ln(x))cos(cos(ln(x)))}{x^{2}(x)} + \frac{sin(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{2}(x)} - \frac{-2cos(ln(x))cos(cos(ln(x)))}{x^{3}} - \frac{-sin(ln(x))cos(cos(ln(x)))}{x^{2}(x)} - \frac{cos(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{2}(x)} - \frac{-2sin(cos(ln(x)))sin^{2}(ln(x))}{x^{3}} - \frac{cos(cos(ln(x)))*-sin(ln(x))sin^{2}(ln(x))}{x^{2}(x)} - \frac{sin(cos(ln(x)))*2sin(ln(x))cos(ln(x))}{x^{2}(x)}\\=&\frac{-sin(ln(x))cos(cos(ln(x)))}{x^{3}} + \frac{3cos(ln(x))cos(cos(ln(x)))}{x^{3}} - \frac{3sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{x^{3}} + \frac{3sin(cos(ln(x)))sin^{2}(ln(x))}{x^{3}} + \frac{sin^{3}(ln(x))cos(cos(ln(x)))}{x^{3}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-sin(ln(x))cos(cos(ln(x)))}{x^{3}} + \frac{3cos(ln(x))cos(cos(ln(x)))}{x^{3}} - \frac{3sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{x^{3}} + \frac{3sin(cos(ln(x)))sin^{2}(ln(x))}{x^{3}} + \frac{sin^{3}(ln(x))cos(cos(ln(x)))}{x^{3}}\right)}{dx}\\=&\frac{--3sin(ln(x))cos(cos(ln(x)))}{x^{4}} - \frac{cos(ln(x))cos(cos(ln(x)))}{x^{3}(x)} - \frac{sin(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{3}(x)} + \frac{3*-3cos(ln(x))cos(cos(ln(x)))}{x^{4}} + \frac{3*-sin(ln(x))cos(cos(ln(x)))}{x^{3}(x)} + \frac{3cos(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{3}(x)} - \frac{3*-3sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{x^{4}} - \frac{3cos(cos(ln(x)))*-sin(ln(x))sin(ln(x))cos(ln(x))}{x^{3}(x)} - \frac{3sin(cos(ln(x)))cos(ln(x))cos(ln(x))}{x^{3}(x)} - \frac{3sin(cos(ln(x)))sin(ln(x))*-sin(ln(x))}{x^{3}(x)} + \frac{3*-3sin(cos(ln(x)))sin^{2}(ln(x))}{x^{4}} + \frac{3cos(cos(ln(x)))*-sin(ln(x))sin^{2}(ln(x))}{x^{3}(x)} + \frac{3sin(cos(ln(x)))*2sin(ln(x))cos(ln(x))}{x^{3}(x)} + \frac{-3sin^{3}(ln(x))cos(cos(ln(x)))}{x^{4}} + \frac{3sin^{2}(ln(x))cos(ln(x))cos(cos(ln(x)))}{x^{3}(x)} + \frac{sin^{3}(ln(x))*-sin(cos(ln(x)))*-sin(ln(x))}{x^{3}(x)}\\=& - \frac{10cos(ln(x))cos(cos(ln(x)))}{x^{4}} + \frac{18sin(cos(ln(x)))sin(ln(x))cos(ln(x))}{x^{4}} + \frac{3sin^{2}(ln(x))cos(ln(x))cos(cos(ln(x)))}{x^{4}} - \frac{7sin(cos(ln(x)))sin^{2}(ln(x))}{x^{4}} + \frac{3sin^{2}(ln(x))cos(cos(ln(x)))cos(ln(x))}{x^{4}} - \frac{3sin(cos(ln(x)))cos^{2}(ln(x))}{x^{4}} - \frac{6sin^{3}(ln(x))cos(cos(ln(x)))}{x^{4}} + \frac{sin(cos(ln(x)))sin^{4}(ln(x))}{x^{4}}\\ \end{split}\end{equation} \]
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