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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{ln(\frac{sin(x)}{x})}{x} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{ln(\frac{sin(x)}{x})}{x}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{ln(\frac{sin(x)}{x})}{x}\right)}{dx}\\=&\frac{-ln(\frac{sin(x)}{x})}{x^{2}} + \frac{(\frac{-sin(x)}{x^{2}} + \frac{cos(x)}{x})}{x(\frac{sin(x)}{x})}\\=&\frac{-ln(\frac{sin(x)}{x})}{x^{2}} + \frac{cos(x)}{xsin(x)} - \frac{1}{x^{2}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-ln(\frac{sin(x)}{x})}{x^{2}} + \frac{cos(x)}{xsin(x)} - \frac{1}{x^{2}}\right)}{dx}\\=&\frac{--2ln(\frac{sin(x)}{x})}{x^{3}} - \frac{(\frac{-sin(x)}{x^{2}} + \frac{cos(x)}{x})}{x^{2}(\frac{sin(x)}{x})} + \frac{-cos(x)}{x^{2}sin(x)} + \frac{-cos(x)cos(x)}{xsin^{2}(x)} + \frac{-sin(x)}{xsin(x)} - \frac{-2}{x^{3}}\\=&\frac{2ln(\frac{sin(x)}{x})}{x^{3}} - \frac{2cos(x)}{x^{2}sin(x)} - \frac{cos^{2}(x)}{xsin^{2}(x)} + \frac{3}{x^{3}} - \frac{1}{x}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2ln(\frac{sin(x)}{x})}{x^{3}} - \frac{2cos(x)}{x^{2}sin(x)} - \frac{cos^{2}(x)}{xsin^{2}(x)} + \frac{3}{x^{3}} - \frac{1}{x}\right)}{dx}\\=&\frac{2*-3ln(\frac{sin(x)}{x})}{x^{4}} + \frac{2(\frac{-sin(x)}{x^{2}} + \frac{cos(x)}{x})}{x^{3}(\frac{sin(x)}{x})} - \frac{2*-2cos(x)}{x^{3}sin(x)} - \frac{2*-cos(x)cos(x)}{x^{2}sin^{2}(x)} - \frac{2*-sin(x)}{x^{2}sin(x)} - \frac{-cos^{2}(x)}{x^{2}sin^{2}(x)} - \frac{-2cos(x)cos^{2}(x)}{xsin^{3}(x)} - \frac{-2cos(x)sin(x)}{xsin^{2}(x)} + \frac{3*-3}{x^{4}} - \frac{-1}{x^{2}}\\=&\frac{-6ln(\frac{sin(x)}{x})}{x^{4}} + \frac{6cos(x)}{x^{3}sin(x)} + \frac{3cos^{2}(x)}{x^{2}sin^{2}(x)} + \frac{2cos(x)}{xsin(x)} + \frac{2cos^{3}(x)}{xsin^{3}(x)} - \frac{11}{x^{4}} + \frac{3}{x^{2}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-6ln(\frac{sin(x)}{x})}{x^{4}} + \frac{6cos(x)}{x^{3}sin(x)} + \frac{3cos^{2}(x)}{x^{2}sin^{2}(x)} + \frac{2cos(x)}{xsin(x)} + \frac{2cos^{3}(x)}{xsin^{3}(x)} - \frac{11}{x^{4}} + \frac{3}{x^{2}}\right)}{dx}\\=&\frac{-6*-4ln(\frac{sin(x)}{x})}{x^{5}} - \frac{6(\frac{-sin(x)}{x^{2}} + \frac{cos(x)}{x})}{x^{4}(\frac{sin(x)}{x})} + \frac{6*-3cos(x)}{x^{4}sin(x)} + \frac{6*-cos(x)cos(x)}{x^{3}sin^{2}(x)} + \frac{6*-sin(x)}{x^{3}sin(x)} + \frac{3*-2cos^{2}(x)}{x^{3}sin^{2}(x)} + \frac{3*-2cos(x)cos^{2}(x)}{x^{2}sin^{3}(x)} + \frac{3*-2cos(x)sin(x)}{x^{2}sin^{2}(x)} + \frac{2*-cos(x)}{x^{2}sin(x)} + \frac{2*-cos(x)cos(x)}{xsin^{2}(x)} + \frac{2*-sin(x)}{xsin(x)} + \frac{2*-cos^{3}(x)}{x^{2}sin^{3}(x)} + \frac{2*-3cos(x)cos^{3}(x)}{xsin^{4}(x)} + \frac{2*-3cos^{2}(x)sin(x)}{xsin^{3}(x)} - \frac{11*-4}{x^{5}} + \frac{3*-2}{x^{3}}\\=&\frac{24ln(\frac{sin(x)}{x})}{x^{5}} - \frac{24cos(x)}{x^{4}sin(x)} - \frac{12cos^{2}(x)}{x^{3}sin^{2}(x)} - \frac{8cos(x)}{x^{2}sin(x)} - \frac{8cos^{3}(x)}{x^{2}sin^{3}(x)} - \frac{8cos^{2}(x)}{xsin^{2}(x)} - \frac{6cos^{4}(x)}{xsin^{4}(x)} - \frac{2}{x} + \frac{50}{x^{5}} - \frac{12}{x^{3}}\\ \end{split}\end{equation} \]
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