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。
\[ \begin{equation}\begin{split}【1/1】求函数log_{tan(x)}^{sin(cos(x))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{tan(x)}^{sin(cos(x))}\right)}{dx}\\=&(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})\\=&\frac{-sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{log_{tan(x)}^{sin(cos(x))}sec^{2}(x)}{ln(tan(x))tan(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{log_{tan(x)}^{sin(cos(x))}sec^{2}(x)}{ln(tan(x))tan(x)}\right)}{dx}\\=&\frac{--sec^{2}(x)(1)sin(x)cos(cos(x))}{ln^{2}(tan(x))(tan(x))sin(cos(x))} - \frac{-cos(cos(x))*-sin(x)sin(x)cos(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{sin(x)*-sin(cos(x))*-sin(x)}{ln(tan(x))sin(cos(x))} - \frac{(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{2}(x)}{ln(tan(x))tan(x)} - \frac{log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))(tan(x))tan(x)} - \frac{log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{2}(x)}{ln(tan(x))tan^{2}(x)} - \frac{log_{tan(x)}^{sin(cos(x))}*2sec^{2}(x)tan(x)}{ln(tan(x))tan(x)}\\=&\frac{2sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{sin^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{sin^{2}(x)}{ln(tan(x))} + \frac{2log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))tan^{2}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}sec^{2}(x)}{ln(tan(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{sin^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{sin^{2}(x)}{ln(tan(x))} + \frac{2log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))tan^{2}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}sec^{2}(x)}{ln(tan(x))}\right)}{dx}\\=&\frac{2*-2sec^{2}(x)(1)sin(x)cos(cos(x))sec^{2}(x)}{ln^{3}(tan(x))(tan(x))sin(cos(x))tan(x)} + \frac{2*-cos(cos(x))*-sin(x)sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{2cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{2sin(x)*-sin(cos(x))*-sin(x)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{2sin(x)cos(cos(x))*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{2sin(x)cos(cos(x))*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{-sec^{2}(x)(1)sin^{2}(x)cos^{2}(cos(x))}{ln^{2}(tan(x))(tan(x))sin^{2}(cos(x))} - \frac{2sin(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin^{2}(x)*-2cos(cos(x))*-sin(x)cos^{2}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} - \frac{sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{-sec^{2}(x)(1)cos(x)cos(cos(x))}{ln^{2}(tan(x))(tan(x))sin(cos(x))} - \frac{-cos(cos(x))*-sin(x)cos(x)cos(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{-sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{cos(x)*-sin(cos(x))*-sin(x)}{ln(tan(x))sin(cos(x))} - \frac{-sec^{2}(x)(1)sin^{2}(x)}{ln^{2}(tan(x))(tan(x))} - \frac{2sin(x)cos(x)}{ln(tan(x))} + \frac{2(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{2log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{3}(tan(x))(tan(x))tan^{2}(x)} + \frac{2log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))tan^{3}(x)} + \frac{2log_{tan(x)}^{sin(cos(x))}*4sec^{4}(x)tan(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{4}(x)}{ln(tan(x))tan^{2}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))(tan(x))tan^{2}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{4}(x)}{ln(tan(x))tan^{3}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}*4sec^{4}(x)tan(x)}{ln(tan(x))tan^{2}(x)} - \frac{2(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{2}(x)}{ln(tan(x))} - \frac{2log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))(tan(x))} - \frac{2log_{tan(x)}^{sin(cos(x))}*2sec^{2}(x)tan(x)}{ln(tan(x))}\\=&\frac{-6sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{3sin^{2}(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3sin^{2}(x)sec^{2}(x)}{ln^{2}(tan(x))tan(x)} - \frac{3sin(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{6sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{2sin(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin(x)cos^{2}(cos(x))cos(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin^{3}(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{2sin^{3}(x)cos^{3}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} + \frac{sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{3sin(x)cos(x)}{ln(tan(x))} - \frac{6log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{3}(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{2}(tan(x))tan^{3}(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))tan(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln(tan(x))tan^{3}(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))tan(x)} - \frac{4log_{tan(x)}^{sin(cos(x))}tan(x)sec^{2}(x)}{ln(tan(x))}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-6sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{3sin^{2}(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3sin^{2}(x)sec^{2}(x)}{ln^{2}(tan(x))tan(x)} - \frac{3sin(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{6sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{2sin(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin(x)cos^{2}(cos(x))cos(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin^{3}(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{2sin^{3}(x)cos^{3}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} + \frac{sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{3sin(x)cos(x)}{ln(tan(x))} - \frac{6log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{3}(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{2}(tan(x))tan^{3}(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))tan(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln(tan(x))tan^{3}(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))tan(x)} - \frac{4log_{tan(x)}^{sin(cos(x))}tan(x)sec^{2}(x)}{ln(tan(x))}\right)}{dx}\\=&\frac{-6*-3sec^{2}(x)(1)sin(x)cos(cos(x))sec^{4}(x)}{ln^{4}(tan(x))(tan(x))sin(cos(x))tan^{2}(x)} - \frac{6*-cos(cos(x))*-sin(x)sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin^{2}(cos(x))tan^{2}(x)} - \frac{6cos(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{6sin(x)*-sin(cos(x))*-sin(x)sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{6sin(x)cos(cos(x))*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{3}(x)} - \frac{6sin(x)cos(cos(x))*4sec^{4}(x)tan(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{3*-2sec^{2}(x)(1)sin^{2}(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{3}(tan(x))(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3*2sin(x)cos(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3sin^{2}(x)*-2cos(cos(x))*-sin(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{3}(cos(x))tan(x)} + \frac{3sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3sin^{2}(x)cos^{2}(cos(x))*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan^{2}(x)} + \frac{3sin^{2}(x)cos^{2}(cos(x))*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3*-2sec^{2}(x)(1)cos(x)cos(cos(x))sec^{2}(x)}{ln^{3}(tan(x))(tan(x))sin(cos(x))tan(x)} + \frac{3*-cos(cos(x))*-sin(x)cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3*-sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3cos(x)*-sin(cos(x))*-sin(x)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3cos(x)cos(cos(x))*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{3cos(x)cos(cos(x))*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3*-2sec^{2}(x)(1)sin^{2}(x)sec^{2}(x)}{ln^{3}(tan(x))(tan(x))tan(x)} + \frac{3*2sin(x)cos(x)sec^{2}(x)}{ln^{2}(tan(x))tan(x)} + \frac{3sin^{2}(x)*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{3sin^{2}(x)*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))tan(x)} - \frac{3*-2sec^{2}(x)(1)sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))(tan(x))sin(cos(x))tan^{2}(x)} - \frac{3*-cos(cos(x))*-sin(x)sin(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan^{2}(x)} - \frac{3cos(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{3sin(x)*-sin(cos(x))*-sin(x)sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{3sin(x)cos(cos(x))*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{3}(x)} - \frac{3sin(x)cos(cos(x))*4sec^{4}(x)tan(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{6*-2sec^{2}(x)(1)sin(x)cos(cos(x))sec^{2}(x)}{ln^{3}(tan(x))(tan(x))sin(cos(x))} + \frac{6*-cos(cos(x))*-sin(x)sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))} + \frac{6cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} + \frac{6sin(x)*-sin(cos(x))*-sin(x)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} + \frac{6sin(x)cos(cos(x))*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{2*-sec^{2}(x)(1)sin(x)cos(x)cos^{2}(cos(x))}{ln^{2}(tan(x))(tan(x))sin^{2}(cos(x))} - \frac{2cos(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin(x)*-2cos(cos(x))*-sin(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} - \frac{2sin(x)*-sin(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin(x)cos(x)*-2cos(cos(x))sin(cos(x))*-sin(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{-sec^{2}(x)(1)sin(x)cos^{2}(cos(x))cos(x)}{ln^{2}(tan(x))(tan(x))sin^{2}(cos(x))} - \frac{cos(x)cos^{2}(cos(x))cos(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin(x)*-2cos(cos(x))*-sin(x)cos^{2}(cos(x))cos(x)}{ln(tan(x))sin^{3}(cos(x))} - \frac{sin(x)*-2cos(cos(x))sin(cos(x))*-sin(x)cos(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin(x)cos^{2}(cos(x))*-sin(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{2*-sec^{2}(x)(1)sin^{3}(x)cos(cos(x))}{ln^{2}(tan(x))(tan(x))sin(cos(x))} - \frac{2*-cos(cos(x))*-sin(x)sin^{3}(x)cos(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{2*3sin^{2}(x)cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{2sin^{3}(x)*-sin(cos(x))*-sin(x)}{ln(tan(x))sin(cos(x))} - \frac{2*-sec^{2}(x)(1)sin^{3}(x)cos^{3}(cos(x))}{ln^{2}(tan(x))(tan(x))sin^{3}(cos(x))} - \frac{2*-3cos(cos(x))*-sin(x)sin^{3}(x)cos^{3}(cos(x))}{ln(tan(x))sin^{4}(cos(x))} - \frac{2*3sin^{2}(x)cos(x)cos^{3}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} - \frac{2sin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)}{ln(tan(x))sin^{3}(cos(x))} + \frac{-sec^{2}(x)(1)sin(x)cos(cos(x))}{ln^{2}(tan(x))(tan(x))sin(cos(x))} + \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} + \frac{sin(x)*-cos(cos(x))*-sin(x)cos(cos(x))}{ln(tan(x))sin^{2}(cos(x))} + \frac{sin(x)*-sin(cos(x))*-sin(x)}{ln(tan(x))sin(cos(x))} - \frac{3*-sec^{2}(x)(1)sin(x)cos(x)}{ln^{2}(tan(x))(tan(x))} - \frac{3cos(x)cos(x)}{ln(tan(x))} - \frac{3sin(x)*-sin(x)}{ln(tan(x))} - \frac{6(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{6}(x)}{ln^{3}(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*-3sec^{2}(x)(1)sec^{6}(x)}{ln^{4}(tan(x))(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*-3sec^{2}(x)(1)sec^{6}(x)}{ln^{3}(tan(x))tan^{4}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*6sec^{6}(x)tan(x)}{ln^{3}(tan(x))tan^{3}(x)} - \frac{6(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{6}(x)}{ln^{2}(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{6}(x)}{ln^{3}(tan(x))(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*-3sec^{2}(x)(1)sec^{6}(x)}{ln^{2}(tan(x))tan^{4}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*6sec^{6}(x)tan(x)}{ln^{2}(tan(x))tan^{3}(x)} + \frac{12(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{4}(x)}{ln^{2}(tan(x))tan(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{3}(tan(x))(tan(x))tan(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}*4sec^{4}(x)tan(x)}{ln^{2}(tan(x))tan(x)} - \frac{2(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{6}(x)}{ln(tan(x))tan^{3}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{6}(x)}{ln^{2}(tan(x))(tan(x))tan^{3}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}*-3sec^{2}(x)(1)sec^{6}(x)}{ln(tan(x))tan^{4}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}*6sec^{6}(x)tan(x)}{ln(tan(x))tan^{3}(x)} + \frac{4(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{4}(x)}{ln(tan(x))tan(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))(tan(x))tan(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{4}(x)}{ln(tan(x))tan^{2}(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}*4sec^{4}(x)tan(x)}{ln(tan(x))tan(x)} - \frac{4(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})tan(x)sec^{2}(x)}{ln(tan(x))} - \frac{4log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)tan(x)sec^{2}(x)}{ln^{2}(tan(x))(tan(x))} - \frac{4log_{tan(x)}^{sin(cos(x))}sec^{2}(x)(1)sec^{2}(x)}{ln(tan(x))} - \frac{4log_{tan(x)}^{sin(cos(x))}tan(x)*2sec^{2}(x)tan(x)}{ln(tan(x))}\\=&\frac{24sin(x)cos(cos(x))sec^{6}(x)}{ln^{4}(tan(x))sin(cos(x))tan^{3}(x)} - \frac{12sin^{2}(x)cos^{2}(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin^{2}(cos(x))tan^{2}(x)} - \frac{12cos(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{12sin^{2}(x)sec^{4}(x)}{ln^{3}(tan(x))tan^{2}(x)} + \frac{24sin(x)cos(cos(x))sec^{6}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{3}(x)} - \frac{48sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan(x)} + \frac{8sin(x)cos(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{8sin^{3}(x)cos^{3}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{3}(cos(x))tan(x)} + \frac{8sin^{3}(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{6sin^{2}(x)cos^{2}(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan^{2}(x)} + \frac{12sin^{2}(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))} + \frac{4sin(x)cos^{2}(cos(x))cos(x)sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{8sin(x)cos(cos(x))sec^{6}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{3}(x)} + \frac{12sin(x)cos(x)sec^{2}(x)}{ln^{2}(tan(x))tan(x)} - \frac{6cos(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{12cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{6sin^{2}(x)sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{12sin^{2}(x)sec^{2}(x)}{ln^{2}(tan(x))} - \frac{4sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{16sin(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{16sin(x)cos(cos(x))tan(x)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{3cos^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{6sin^{2}(x)cos^{3}(cos(x))cos(x)}{ln(tan(x))sin^{3}(cos(x))} - \frac{6sin^{2}(x)cos(cos(x))cos(x)}{ln(tan(x))sin(cos(x))} - \frac{6sin^{2}(x)cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{6sin^{2}(x)cos(x)cos^{3}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} + \frac{3sin^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{6sin^{4}(x)cos^{4}(cos(x))}{ln(tan(x))sin^{4}(cos(x))} - \frac{8sin^{4}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} + \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} + \frac{sin^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin^{4}(x)}{ln(tan(x))} + \frac{4sin^{2}(x)}{ln(tan(x))} - \frac{3cos^{2}(x)}{ln(tan(x))} + \frac{24log_{tan(x)}^{sin(cos(x))}sec^{8}(x)}{ln^{4}(tan(x))tan^{4}(x)} + \frac{36log_{tan(x)}^{sin(cos(x))}sec^{8}(x)}{ln^{3}(tan(x))tan^{4}(x)} - \frac{72log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{3}(tan(x))tan^{2}(x)} + \frac{22log_{tan(x)}^{sin(cos(x))}sec^{8}(x)}{ln^{2}(tan(x))tan^{4}(x)} - \frac{56log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{56log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))} + \frac{6log_{tan(x)}^{sin(cos(x))}sec^{8}(x)}{ln(tan(x))tan^{4}(x)} - \frac{16log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln(tan(x))tan^{2}(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))} - \frac{8log_{tan(x)}^{sin(cos(x))}tan^{2}(x)sec^{2}(x)}{ln(tan(x))}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数log_{tan(x)}^{sin(cos(x))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{tan(x)}^{sin(cos(x))}\right)}{dx}\\=&(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})\\=&\frac{-sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{log_{tan(x)}^{sin(cos(x))}sec^{2}(x)}{ln(tan(x))tan(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{log_{tan(x)}^{sin(cos(x))}sec^{2}(x)}{ln(tan(x))tan(x)}\right)}{dx}\\=&\frac{--sec^{2}(x)(1)sin(x)cos(cos(x))}{ln^{2}(tan(x))(tan(x))sin(cos(x))} - \frac{-cos(cos(x))*-sin(x)sin(x)cos(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{sin(x)*-sin(cos(x))*-sin(x)}{ln(tan(x))sin(cos(x))} - \frac{(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{2}(x)}{ln(tan(x))tan(x)} - \frac{log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))(tan(x))tan(x)} - \frac{log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{2}(x)}{ln(tan(x))tan^{2}(x)} - \frac{log_{tan(x)}^{sin(cos(x))}*2sec^{2}(x)tan(x)}{ln(tan(x))tan(x)}\\=&\frac{2sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{sin^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{sin^{2}(x)}{ln(tan(x))} + \frac{2log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))tan^{2}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}sec^{2}(x)}{ln(tan(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{2sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{sin^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{sin^{2}(x)}{ln(tan(x))} + \frac{2log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))tan^{2}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}sec^{2}(x)}{ln(tan(x))}\right)}{dx}\\=&\frac{2*-2sec^{2}(x)(1)sin(x)cos(cos(x))sec^{2}(x)}{ln^{3}(tan(x))(tan(x))sin(cos(x))tan(x)} + \frac{2*-cos(cos(x))*-sin(x)sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{2cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{2sin(x)*-sin(cos(x))*-sin(x)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{2sin(x)cos(cos(x))*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{2sin(x)cos(cos(x))*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{-sec^{2}(x)(1)sin^{2}(x)cos^{2}(cos(x))}{ln^{2}(tan(x))(tan(x))sin^{2}(cos(x))} - \frac{2sin(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin^{2}(x)*-2cos(cos(x))*-sin(x)cos^{2}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} - \frac{sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{-sec^{2}(x)(1)cos(x)cos(cos(x))}{ln^{2}(tan(x))(tan(x))sin(cos(x))} - \frac{-cos(cos(x))*-sin(x)cos(x)cos(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{-sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{cos(x)*-sin(cos(x))*-sin(x)}{ln(tan(x))sin(cos(x))} - \frac{-sec^{2}(x)(1)sin^{2}(x)}{ln^{2}(tan(x))(tan(x))} - \frac{2sin(x)cos(x)}{ln(tan(x))} + \frac{2(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{2log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{3}(tan(x))(tan(x))tan^{2}(x)} + \frac{2log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))tan^{3}(x)} + \frac{2log_{tan(x)}^{sin(cos(x))}*4sec^{4}(x)tan(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{4}(x)}{ln(tan(x))tan^{2}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))(tan(x))tan^{2}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{4}(x)}{ln(tan(x))tan^{3}(x)} + \frac{log_{tan(x)}^{sin(cos(x))}*4sec^{4}(x)tan(x)}{ln(tan(x))tan^{2}(x)} - \frac{2(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{2}(x)}{ln(tan(x))} - \frac{2log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))(tan(x))} - \frac{2log_{tan(x)}^{sin(cos(x))}*2sec^{2}(x)tan(x)}{ln(tan(x))}\\=&\frac{-6sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{3sin^{2}(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3sin^{2}(x)sec^{2}(x)}{ln^{2}(tan(x))tan(x)} - \frac{3sin(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{6sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{2sin(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin(x)cos^{2}(cos(x))cos(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin^{3}(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{2sin^{3}(x)cos^{3}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} + \frac{sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{3sin(x)cos(x)}{ln(tan(x))} - \frac{6log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{3}(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{2}(tan(x))tan^{3}(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))tan(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln(tan(x))tan^{3}(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))tan(x)} - \frac{4log_{tan(x)}^{sin(cos(x))}tan(x)sec^{2}(x)}{ln(tan(x))}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-6sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{3sin^{2}(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3sin^{2}(x)sec^{2}(x)}{ln^{2}(tan(x))tan(x)} - \frac{3sin(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{6sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{2sin(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin(x)cos^{2}(cos(x))cos(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin^{3}(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{2sin^{3}(x)cos^{3}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} + \frac{sin(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{3sin(x)cos(x)}{ln(tan(x))} - \frac{6log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{3}(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{2}(tan(x))tan^{3}(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))tan(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln(tan(x))tan^{3}(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))tan(x)} - \frac{4log_{tan(x)}^{sin(cos(x))}tan(x)sec^{2}(x)}{ln(tan(x))}\right)}{dx}\\=&\frac{-6*-3sec^{2}(x)(1)sin(x)cos(cos(x))sec^{4}(x)}{ln^{4}(tan(x))(tan(x))sin(cos(x))tan^{2}(x)} - \frac{6*-cos(cos(x))*-sin(x)sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin^{2}(cos(x))tan^{2}(x)} - \frac{6cos(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{6sin(x)*-sin(cos(x))*-sin(x)sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{6sin(x)cos(cos(x))*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{3}(x)} - \frac{6sin(x)cos(cos(x))*4sec^{4}(x)tan(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{3*-2sec^{2}(x)(1)sin^{2}(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{3}(tan(x))(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3*2sin(x)cos(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3sin^{2}(x)*-2cos(cos(x))*-sin(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{3}(cos(x))tan(x)} + \frac{3sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3sin^{2}(x)cos^{2}(cos(x))*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan^{2}(x)} + \frac{3sin^{2}(x)cos^{2}(cos(x))*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3*-2sec^{2}(x)(1)cos(x)cos(cos(x))sec^{2}(x)}{ln^{3}(tan(x))(tan(x))sin(cos(x))tan(x)} + \frac{3*-cos(cos(x))*-sin(x)cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{3*-sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3cos(x)*-sin(cos(x))*-sin(x)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3cos(x)cos(cos(x))*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{3cos(x)cos(cos(x))*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{3*-2sec^{2}(x)(1)sin^{2}(x)sec^{2}(x)}{ln^{3}(tan(x))(tan(x))tan(x)} + \frac{3*2sin(x)cos(x)sec^{2}(x)}{ln^{2}(tan(x))tan(x)} + \frac{3sin^{2}(x)*-sec^{2}(x)(1)sec^{2}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{3sin^{2}(x)*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))tan(x)} - \frac{3*-2sec^{2}(x)(1)sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))(tan(x))sin(cos(x))tan^{2}(x)} - \frac{3*-cos(cos(x))*-sin(x)sin(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan^{2}(x)} - \frac{3cos(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{3sin(x)*-sin(cos(x))*-sin(x)sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{3sin(x)cos(cos(x))*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{3}(x)} - \frac{3sin(x)cos(cos(x))*4sec^{4}(x)tan(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{6*-2sec^{2}(x)(1)sin(x)cos(cos(x))sec^{2}(x)}{ln^{3}(tan(x))(tan(x))sin(cos(x))} + \frac{6*-cos(cos(x))*-sin(x)sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))} + \frac{6cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} + \frac{6sin(x)*-sin(cos(x))*-sin(x)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} + \frac{6sin(x)cos(cos(x))*2sec^{2}(x)tan(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{2*-sec^{2}(x)(1)sin(x)cos(x)cos^{2}(cos(x))}{ln^{2}(tan(x))(tan(x))sin^{2}(cos(x))} - \frac{2cos(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin(x)*-2cos(cos(x))*-sin(x)cos(x)cos^{2}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} - \frac{2sin(x)*-sin(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin(x)cos(x)*-2cos(cos(x))sin(cos(x))*-sin(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{-sec^{2}(x)(1)sin(x)cos^{2}(cos(x))cos(x)}{ln^{2}(tan(x))(tan(x))sin^{2}(cos(x))} - \frac{cos(x)cos^{2}(cos(x))cos(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin(x)*-2cos(cos(x))*-sin(x)cos^{2}(cos(x))cos(x)}{ln(tan(x))sin^{3}(cos(x))} - \frac{sin(x)*-2cos(cos(x))sin(cos(x))*-sin(x)cos(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{sin(x)cos^{2}(cos(x))*-sin(x)}{ln(tan(x))sin^{2}(cos(x))} - \frac{2*-sec^{2}(x)(1)sin^{3}(x)cos(cos(x))}{ln^{2}(tan(x))(tan(x))sin(cos(x))} - \frac{2*-cos(cos(x))*-sin(x)sin^{3}(x)cos(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{2*3sin^{2}(x)cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{2sin^{3}(x)*-sin(cos(x))*-sin(x)}{ln(tan(x))sin(cos(x))} - \frac{2*-sec^{2}(x)(1)sin^{3}(x)cos^{3}(cos(x))}{ln^{2}(tan(x))(tan(x))sin^{3}(cos(x))} - \frac{2*-3cos(cos(x))*-sin(x)sin^{3}(x)cos^{3}(cos(x))}{ln(tan(x))sin^{4}(cos(x))} - \frac{2*3sin^{2}(x)cos(x)cos^{3}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} - \frac{2sin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)}{ln(tan(x))sin^{3}(cos(x))} + \frac{-sec^{2}(x)(1)sin(x)cos(cos(x))}{ln^{2}(tan(x))(tan(x))sin(cos(x))} + \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} + \frac{sin(x)*-cos(cos(x))*-sin(x)cos(cos(x))}{ln(tan(x))sin^{2}(cos(x))} + \frac{sin(x)*-sin(cos(x))*-sin(x)}{ln(tan(x))sin(cos(x))} - \frac{3*-sec^{2}(x)(1)sin(x)cos(x)}{ln^{2}(tan(x))(tan(x))} - \frac{3cos(x)cos(x)}{ln(tan(x))} - \frac{3sin(x)*-sin(x)}{ln(tan(x))} - \frac{6(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{6}(x)}{ln^{3}(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*-3sec^{2}(x)(1)sec^{6}(x)}{ln^{4}(tan(x))(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*-3sec^{2}(x)(1)sec^{6}(x)}{ln^{3}(tan(x))tan^{4}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*6sec^{6}(x)tan(x)}{ln^{3}(tan(x))tan^{3}(x)} - \frac{6(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{6}(x)}{ln^{2}(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{6}(x)}{ln^{3}(tan(x))(tan(x))tan^{3}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*-3sec^{2}(x)(1)sec^{6}(x)}{ln^{2}(tan(x))tan^{4}(x)} - \frac{6log_{tan(x)}^{sin(cos(x))}*6sec^{6}(x)tan(x)}{ln^{2}(tan(x))tan^{3}(x)} + \frac{12(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{4}(x)}{ln^{2}(tan(x))tan(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}*-2sec^{2}(x)(1)sec^{4}(x)}{ln^{3}(tan(x))(tan(x))tan(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}*4sec^{4}(x)tan(x)}{ln^{2}(tan(x))tan(x)} - \frac{2(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{6}(x)}{ln(tan(x))tan^{3}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{6}(x)}{ln^{2}(tan(x))(tan(x))tan^{3}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}*-3sec^{2}(x)(1)sec^{6}(x)}{ln(tan(x))tan^{4}(x)} - \frac{2log_{tan(x)}^{sin(cos(x))}*6sec^{6}(x)tan(x)}{ln(tan(x))tan^{3}(x)} + \frac{4(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})sec^{4}(x)}{ln(tan(x))tan(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{4}(x)}{ln^{2}(tan(x))(tan(x))tan(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)sec^{4}(x)}{ln(tan(x))tan^{2}(x)} + \frac{4log_{tan(x)}^{sin(cos(x))}*4sec^{4}(x)tan(x)}{ln(tan(x))tan(x)} - \frac{4(\frac{(\frac{(cos(cos(x))*-sin(x))}{(sin(cos(x)))} - \frac{(sec^{2}(x)(1))log_{tan(x)}^{sin(cos(x))}}{(tan(x))})}{(ln(tan(x)))})tan(x)sec^{2}(x)}{ln(tan(x))} - \frac{4log_{tan(x)}^{sin(cos(x))}*-sec^{2}(x)(1)tan(x)sec^{2}(x)}{ln^{2}(tan(x))(tan(x))} - \frac{4log_{tan(x)}^{sin(cos(x))}sec^{2}(x)(1)sec^{2}(x)}{ln(tan(x))} - \frac{4log_{tan(x)}^{sin(cos(x))}tan(x)*2sec^{2}(x)tan(x)}{ln(tan(x))}\\=&\frac{24sin(x)cos(cos(x))sec^{6}(x)}{ln^{4}(tan(x))sin(cos(x))tan^{3}(x)} - \frac{12sin^{2}(x)cos^{2}(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin^{2}(cos(x))tan^{2}(x)} - \frac{12cos(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{2}(x)} - \frac{12sin^{2}(x)sec^{4}(x)}{ln^{3}(tan(x))tan^{2}(x)} + \frac{24sin(x)cos(cos(x))sec^{6}(x)}{ln^{3}(tan(x))sin(cos(x))tan^{3}(x)} - \frac{48sin(x)cos(cos(x))sec^{4}(x)}{ln^{3}(tan(x))sin(cos(x))tan(x)} + \frac{8sin(x)cos(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{8sin^{3}(x)cos^{3}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{3}(cos(x))tan(x)} + \frac{8sin^{3}(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{6sin^{2}(x)cos^{2}(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan^{2}(x)} + \frac{12sin^{2}(x)cos^{2}(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))} + \frac{4sin(x)cos^{2}(cos(x))cos(x)sec^{2}(x)}{ln^{2}(tan(x))sin^{2}(cos(x))tan(x)} + \frac{8sin(x)cos(cos(x))sec^{6}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{3}(x)} + \frac{12sin(x)cos(x)sec^{2}(x)}{ln^{2}(tan(x))tan(x)} - \frac{6cos(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan^{2}(x)} + \frac{12cos(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{6sin^{2}(x)sec^{4}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{12sin^{2}(x)sec^{2}(x)}{ln^{2}(tan(x))} - \frac{4sin(x)cos(cos(x))sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} - \frac{16sin(x)cos(cos(x))sec^{4}(x)}{ln^{2}(tan(x))sin(cos(x))tan(x)} + \frac{16sin(x)cos(cos(x))tan(x)sec^{2}(x)}{ln^{2}(tan(x))sin(cos(x))} - \frac{3cos^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{6sin^{2}(x)cos^{3}(cos(x))cos(x)}{ln(tan(x))sin^{3}(cos(x))} - \frac{6sin^{2}(x)cos(cos(x))cos(x)}{ln(tan(x))sin(cos(x))} - \frac{6sin^{2}(x)cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} - \frac{6sin^{2}(x)cos(x)cos^{3}(cos(x))}{ln(tan(x))sin^{3}(cos(x))} + \frac{3sin^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{6sin^{4}(x)cos^{4}(cos(x))}{ln(tan(x))sin^{4}(cos(x))} - \frac{8sin^{4}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} + \frac{cos(x)cos(cos(x))}{ln(tan(x))sin(cos(x))} + \frac{sin^{2}(x)cos^{2}(cos(x))}{ln(tan(x))sin^{2}(cos(x))} - \frac{2sin^{4}(x)}{ln(tan(x))} + \frac{4sin^{2}(x)}{ln(tan(x))} - \frac{3cos^{2}(x)}{ln(tan(x))} + \frac{24log_{tan(x)}^{sin(cos(x))}sec^{8}(x)}{ln^{4}(tan(x))tan^{4}(x)} + \frac{36log_{tan(x)}^{sin(cos(x))}sec^{8}(x)}{ln^{3}(tan(x))tan^{4}(x)} - \frac{72log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{3}(tan(x))tan^{2}(x)} + \frac{22log_{tan(x)}^{sin(cos(x))}sec^{8}(x)}{ln^{2}(tan(x))tan^{4}(x)} - \frac{56log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln^{2}(tan(x))tan^{2}(x)} + \frac{56log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln^{2}(tan(x))} + \frac{6log_{tan(x)}^{sin(cos(x))}sec^{8}(x)}{ln(tan(x))tan^{4}(x)} - \frac{16log_{tan(x)}^{sin(cos(x))}sec^{6}(x)}{ln(tan(x))tan^{2}(x)} + \frac{12log_{tan(x)}^{sin(cos(x))}sec^{4}(x)}{ln(tan(x))} - \frac{8log_{tan(x)}^{sin(cos(x))}tan^{2}(x)sec^{2}(x)}{ln(tan(x))}\\ \end{split}\end{equation} \]
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