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。
\[ \begin{equation}\begin{split}【1/1】求函数log_{th(x)}^{sh(ch(x))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{th(x)}^{sh(ch(x))}\right)}{dx}\\=&(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})\\=&\frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{log_{th(x)}^{sh(ch(x))}th(x)}{ln(th(x))} - \frac{log_{th(x)}^{sh(ch(x))}}{ln(th(x))th(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{log_{th(x)}^{sh(ch(x))}th(x)}{ln(th(x))} - \frac{log_{th(x)}^{sh(ch(x))}}{ln(th(x))th(x)}\right)}{dx}\\=&\frac{-(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{2}(th(x))(th(x))sh(ch(x))} + \frac{-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{sh(x)sh(ch(x))sh(x)}{ln(th(x))sh(ch(x))} + \frac{(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th(x)}{ln(th(x))} + \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))th(x)}{ln^{2}(th(x))(th(x))} + \frac{log_{th(x)}^{sh(ch(x))}(1 - th^{2}(x))}{ln(th(x))} - \frac{(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln(th(x))th(x)} - \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))(th(x))th(x)} - \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln(th(x))th^{2}(x)}\\=&\frac{-2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} + \frac{2sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{sh^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{sh^{2}(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{2}(th(x))} + \frac{log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{2}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{2}(x)} - \frac{log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln(th(x))} - \frac{4log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} + \frac{2sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{sh^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{sh^{2}(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{2}(th(x))} + \frac{log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{2}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{2}(x)} - \frac{log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln(th(x))} - \frac{4log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))}\right)}{dx}\\=&\frac{-2*-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))th(x)} - \frac{2*-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} - \frac{2ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{2sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{2sh(x)ch(ch(x))*-(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{2*-2(1 - th^{2}(x))sh(x)ch(ch(x))th(x)}{ln^{3}(th(x))(th(x))sh(ch(x))} + \frac{2*-ch(ch(x))sh(x)sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{2ch(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh(x)sh(ch(x))sh(x)th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh(x)ch(ch(x))(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))} - \frac{-(1 - th^{2}(x))sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))(th(x))sh^{2}(ch(x))} - \frac{2sh(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{sh^{2}(x)*-2ch(ch(x))sh(x)ch^{2}(ch(x))}{ln(th(x))sh^{3}(ch(x))} - \frac{sh^{2}(x)*2ch(ch(x))sh(ch(x))sh(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{-(1 - th^{2}(x))ch(x)ch(ch(x))}{ln^{2}(th(x))(th(x))sh(ch(x))} + \frac{-ch(ch(x))sh(x)ch(x)ch(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{ch(x)sh(ch(x))sh(x)}{ln(th(x))sh(ch(x))} + \frac{-(1 - th^{2}(x))sh^{2}(x)}{ln^{2}(th(x))(th(x))} + \frac{2sh(x)ch(x)}{ln(th(x))} + \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{2}(x)}{ln^{2}(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))th^{2}(x)}{ln^{3}(th(x))(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}*2th(x)(1 - th^{2}(x))}{ln^{2}(th(x))} + \frac{(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln(th(x))th^{2}(x)} + \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))(th(x))th^{2}(x)} + \frac{log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln(th(x))th^{3}(x)} + \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{2}(th(x))th^{2}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{3}(th(x))(th(x))th^{2}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{2}(th(x))th^{3}(x)} - \frac{(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{2}(x)}{ln(th(x))} - \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))th^{2}(x)}{ln^{2}(th(x))(th(x))} - \frac{log_{th(x)}^{sh(ch(x))}*2th(x)(1 - th^{2}(x))}{ln(th(x))} - \frac{4(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{2}(th(x))} - \frac{4log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{3}(th(x))(th(x))}\\=&\frac{6sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{3sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{3ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{3sh^{2}(x)}{ln^{2}(th(x))th(x)} + \frac{6sh(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} - \frac{3sh^{2}(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3sh(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{2sh(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{3ch(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{3sh^{2}(x)th(x)}{ln^{2}(th(x))} - \frac{sh(x)ch^{2}(ch(x))ch(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh^{3}(x)ch^{3}(ch(x))}{ln(th(x))sh^{3}(ch(x))} - \frac{2sh^{3}(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{3sh(x)ch(x)}{ln(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th(x)} - \frac{18log_{th(x)}^{sh(ch(x))}th(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}th(x)}{ln^{2}(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln^{2}(th(x))} - \frac{12sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))} + \frac{18log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th(x)} - \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{3}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}}{ln(th(x))th(x)} - \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}th(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln(th(x))}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{6sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{3sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{3ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{3sh^{2}(x)}{ln^{2}(th(x))th(x)} + \frac{6sh(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} - \frac{3sh^{2}(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3sh(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{2sh(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{3ch(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{3sh^{2}(x)th(x)}{ln^{2}(th(x))} - \frac{sh(x)ch^{2}(ch(x))ch(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh^{3}(x)ch^{3}(ch(x))}{ln(th(x))sh^{3}(ch(x))} - \frac{2sh^{3}(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{3sh(x)ch(x)}{ln(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th(x)} - \frac{18log_{th(x)}^{sh(ch(x))}th(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}th(x)}{ln^{2}(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln^{2}(th(x))} - \frac{12sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))} + \frac{18log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th(x)} - \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{3}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}}{ln(th(x))th(x)} - \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}th(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln(th(x))}\right)}{dx}\\=&\frac{6*-3(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{4}(th(x))(th(x))sh(ch(x))th^{2}(x)} + \frac{6*-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{3}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{6ch(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{6sh(x)sh(ch(x))sh(x)}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{6sh(x)ch(ch(x))*-2(1 - th^{2}(x))}{ln^{3}(th(x))sh(ch(x))th^{3}(x)} + \frac{3*-2(1 - th^{2}(x))sh^{2}(x)ch^{2}(ch(x))}{ln^{3}(th(x))(th(x))sh^{2}(ch(x))th(x)} + \frac{3*2sh(x)ch(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{3sh^{2}(x)*-2ch(ch(x))sh(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{3}(ch(x))th(x)} + \frac{3sh^{2}(x)*2ch(ch(x))sh(ch(x))sh(x)}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{3sh^{2}(x)ch^{2}(ch(x))*-(1 - th^{2}(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{2*-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))th^{2}(x)} + \frac{2ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{2sh(x)*-ch(ch(x))sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{2sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{2sh(x)ch(ch(x))*-2(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))th^{3}(x)} - \frac{3*-2(1 - th^{2}(x))ch(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))th(x)} - \frac{3*-ch(ch(x))sh(x)ch(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} - \frac{3sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{3ch(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{3ch(x)ch(ch(x))*-(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{3*-2(1 - th^{2}(x))sh^{2}(x)}{ln^{3}(th(x))(th(x))th(x)} - \frac{3*2sh(x)ch(x)}{ln^{2}(th(x))th(x)} - \frac{3sh^{2}(x)*-(1 - th^{2}(x))}{ln^{2}(th(x))th^{2}(x)} + \frac{6*-3(1 - th^{2}(x))sh(x)ch(ch(x))th^{2}(x)}{ln^{4}(th(x))(th(x))sh(ch(x))} + \frac{6*-ch(ch(x))sh(x)sh(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh^{2}(ch(x))} + \frac{6ch(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{6sh(x)sh(ch(x))sh(x)th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{6sh(x)ch(ch(x))*2th(x)(1 - th^{2}(x))}{ln^{3}(th(x))sh(ch(x))} - \frac{3*-2(1 - th^{2}(x))sh^{2}(x)ch^{2}(ch(x))th(x)}{ln^{3}(th(x))(th(x))sh^{2}(ch(x))} - \frac{3*2sh(x)ch(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3sh^{2}(x)*-2ch(ch(x))sh(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{3}(ch(x))} - \frac{3sh^{2}(x)*2ch(ch(x))sh(ch(x))sh(x)th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3sh^{2}(x)ch^{2}(ch(x))(1 - th^{2}(x))}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3*-2(1 - th^{2}(x))sh(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))(th(x))sh(ch(x))} - \frac{3*-ch(ch(x))sh(x)sh(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3ch(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{3sh(x)sh(ch(x))sh(x)th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{3sh(x)ch(ch(x))*2th(x)(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))} - \frac{2*-(1 - th^{2}(x))sh(x)ch(x)ch^{2}(ch(x))}{ln^{2}(th(x))(th(x))sh^{2}(ch(x))} - \frac{2ch(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{2sh(x)*-2ch(ch(x))sh(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{3}(ch(x))} - \frac{2sh(x)sh(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{2sh(x)ch(x)*2ch(ch(x))sh(ch(x))sh(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{3*-2(1 - th^{2}(x))ch(x)ch(ch(x))th(x)}{ln^{3}(th(x))(th(x))sh(ch(x))} + \frac{3*-ch(ch(x))sh(x)ch(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{3sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{3ch(x)sh(ch(x))sh(x)th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{3ch(x)ch(ch(x))(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{3*-2(1 - th^{2}(x))sh^{2}(x)th(x)}{ln^{3}(th(x))(th(x))} + \frac{3*2sh(x)ch(x)th(x)}{ln^{2}(th(x))} + \frac{3sh^{2}(x)(1 - th^{2}(x))}{ln^{2}(th(x))} - \frac{-(1 - th^{2}(x))sh(x)ch^{2}(ch(x))ch(x)}{ln^{2}(th(x))(th(x))sh^{2}(ch(x))} - \frac{ch(x)ch^{2}(ch(x))ch(x)}{ln(th(x))sh^{2}(ch(x))} - \frac{sh(x)*-2ch(ch(x))sh(x)ch^{2}(ch(x))ch(x)}{ln(th(x))sh^{3}(ch(x))} - \frac{sh(x)*2ch(ch(x))sh(ch(x))sh(x)ch(x)}{ln(th(x))sh^{2}(ch(x))} - \frac{sh(x)ch^{2}(ch(x))sh(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))th^{2}(x)} + \frac{-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{sh(x)ch(ch(x))*-2(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))th^{3}(x)} - \frac{2*-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))} - \frac{2*-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{2ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} - \frac{2sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{2*-(1 - th^{2}(x))sh^{3}(x)ch^{3}(ch(x))}{ln^{2}(th(x))(th(x))sh^{3}(ch(x))} + \frac{2*-3ch(ch(x))sh(x)sh^{3}(x)ch^{3}(ch(x))}{ln(th(x))sh^{4}(ch(x))} + \frac{2*3sh^{2}(x)ch(x)ch^{3}(ch(x))}{ln(th(x))sh^{3}(ch(x))} + \frac{2sh^{3}(x)*3ch^{2}(ch(x))sh(ch(x))sh(x)}{ln(th(x))sh^{3}(ch(x))} - \frac{2*-(1 - th^{2}(x))sh^{3}(x)ch(ch(x))}{ln^{2}(th(x))(th(x))sh(ch(x))} - \frac{2*-ch(ch(x))sh(x)sh^{3}(x)ch(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{2*3sh^{2}(x)ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} - \frac{2sh^{3}(x)sh(ch(x))sh(x)}{ln(th(x))sh(ch(x))} + \frac{2*-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))} + \frac{2ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh(x)*-ch(ch(x))sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{2sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{-(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{2}(th(x))(th(x))sh(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{sh(x)*-ch(ch(x))sh(x)ch(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{sh(x)sh(ch(x))sh(x)}{ln(th(x))sh(ch(x))} + \frac{3*-(1 - th^{2}(x))sh(x)ch(x)}{ln^{2}(th(x))(th(x))} + \frac{3ch(x)ch(x)}{ln(th(x))} + \frac{3sh(x)sh(x)}{ln(th(x))} + \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{3}(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))th^{3}(x)}{ln^{4}(th(x))(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}*3th^{2}(x)(1 - th^{2}(x))}{ln^{3}(th(x))} + \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{2}(th(x))th(x)} + \frac{6log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{3}(th(x))(th(x))th(x)} + \frac{6log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))th^{2}(x)} - \frac{18(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th(x)}{ln^{3}(th(x))} - \frac{18log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))th(x)}{ln^{4}(th(x))(th(x))} - \frac{18log_{th(x)}^{sh(ch(x))}(1 - th^{2}(x))}{ln^{3}(th(x))} + \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th(x)}{ln^{2}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))th(x)}{ln^{3}(th(x))(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}(1 - th^{2}(x))}{ln^{2}(th(x))} - \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{3}(x)}{ln^{2}(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))th^{3}(x)}{ln^{3}(th(x))(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}*3th^{2}(x)(1 - th^{2}(x))}{ln^{2}(th(x))} - \frac{12*-3(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{4}(th(x))(th(x))sh(ch(x))} - \frac{12*-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{3}(th(x))sh^{2}(ch(x))} - \frac{12ch(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))} - \frac{12sh(x)sh(ch(x))sh(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{18(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{3}(th(x))th(x)} + \frac{18log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln^{4}(th(x))(th(x))th(x)} + \frac{18log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{3}(th(x))th^{2}(x)} - \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{2}(th(x))th^{3}(x)} - \frac{6log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{3}(th(x))(th(x))th^{3}(x)} - \frac{6log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln^{2}(th(x))th^{4}(x)} - \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln(th(x))th^{4}(x)} + \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln(th(x))th(x)} + \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))(th(x))th(x)} + \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln(th(x))th^{2}(x)} - \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{3}(th(x))th^{3}(x)} - \frac{6log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln^{4}(th(x))(th(x))th^{3}(x)} - \frac{6log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln^{3}(th(x))th^{4}(x)} - \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th(x)}{ln(th(x))} - \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))th(x)}{ln^{2}(th(x))(th(x))} - \frac{2log_{th(x)}^{sh(ch(x))}(1 - th^{2}(x))}{ln(th(x))} + \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{3}(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))th^{3}(x)}{ln^{2}(th(x))(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}*3th^{2}(x)(1 - th^{2}(x))}{ln(th(x))}\\=&\frac{-24sh(x)ch(ch(x))}{ln^{4}(th(x))sh(ch(x))th^{3}(x)} + \frac{72sh(x)ch(ch(x))}{ln^{4}(th(x))sh(ch(x))th(x)} - \frac{12sh^{2}(x)ch^{2}(ch(x))}{ln^{3}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{3ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{12sh^{2}(x)}{ln^{3}(th(x))th^{2}(x)} - \frac{16sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{3}(x)} + \frac{24sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th(x)} + \frac{8sh(x)ch(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} - \frac{8sh^{3}(x)ch^{3}(ch(x))}{ln^{2}(th(x))sh^{3}(ch(x))th(x)} + \frac{8sh^{3}(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{5sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} - \frac{6sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{3}(x)} + \frac{4sh(x)ch^{2}(ch(x))ch(x)}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{12ch(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{6sh^{2}(x)}{ln^{2}(th(x))th^{2}(x)} - \frac{24sh(x)ch(ch(x))th^{3}(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{3ch(ch(x))ch(x)}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{12ch(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} - \frac{72sh(x)ch(ch(x))th(x)}{ln^{4}(th(x))sh(ch(x))} + \frac{24sh(x)ch(ch(x))th^{3}(x)}{ln^{4}(th(x))sh(ch(x))} - \frac{12sh(x)ch(x)}{ln^{2}(th(x))th(x)} - \frac{6ch(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{12sh^{2}(x)ch^{2}(ch(x))th^{2}(x)}{ln^{3}(th(x))sh^{2}(ch(x))} + \frac{16sh(x)ch(ch(x))th(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{8sh(x)ch(ch(x))th^{3}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{24ch(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))} + \frac{12sh^{2}(x)th^{2}(x)}{ln^{3}(th(x))} - \frac{8sh(x)ch(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{8sh^{3}(x)ch^{3}(ch(x))th(x)}{ln^{2}(th(x))sh^{3}(ch(x))} - \frac{8sh^{3}(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{2sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{4sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} + \frac{8sh(x)ch(ch(x))th(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{6sh^{2}(x)ch^{2}(ch(x))th^{2}(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{3}(x)} - \frac{4sh(x)ch^{2}(ch(x))ch(x)th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} - \frac{6sh^{2}(x)th^{2}(x)}{ln^{2}(th(x))} - \frac{6sh^{2}(x)ch(ch(x))ch(x)}{ln(th(x))sh(ch(x))} - \frac{3ch^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{6sh^{2}(x)ch^{3}(ch(x))ch(x)}{ln(th(x))sh^{3}(ch(x))} - \frac{8sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{3}(x)} - \frac{sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{6sh^{2}(x)ch(x)ch^{3}(ch(x))}{ln(th(x))sh^{3}(ch(x))} + \frac{12sh(x)ch(x)th(x)}{ln^{2}(th(x))} + \frac{3ch(ch(x))ch(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{6sh^{2}(x)ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} - \frac{2sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{5sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{8sh^{4}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{6sh^{4}(x)ch^{4}(ch(x))}{ln(th(x))sh^{4}(ch(x))} + \frac{24sh^{2}(x)ch^{2}(ch(x))}{ln^{3}(th(x))sh^{2}(ch(x))} - \frac{5sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} - \frac{sh^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{3sh^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{2sh^{4}(x)}{ln(th(x))} + \frac{4sh^{2}(x)}{ln(th(x))} + \frac{3ch^{2}(x)}{ln(th(x))} + \frac{24log_{th(x)}^{sh(ch(x))}th^{4}(x)}{ln^{4}(th(x))} - \frac{96log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{4}(th(x))} + \frac{72log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{3}(th(x))} - \frac{36log_{th(x)}^{sh(ch(x))}th^{4}(x)}{ln^{3}(th(x))} - \frac{72log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th^{2}(x)} - \frac{32log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{2}(x)} - \frac{32log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{2}(th(x))} + \frac{22log_{th(x)}^{sh(ch(x))}th^{4}(x)}{ln^{2}(th(x))} + \frac{22log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{4}(x)} - \frac{96log_{th(x)}^{sh(ch(x))}}{ln^{4}(th(x))th^{2}(x)} + \frac{6log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{4}(x)} - \frac{8log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{2}(x)} + \frac{36log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th^{4}(x)} + \frac{8log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}th^{4}(x)}{ln(th(x))} + \frac{24log_{th(x)}^{sh(ch(x))}}{ln^{4}(th(x))th^{4}(x)} + \frac{144log_{th(x)}^{sh(ch(x))}}{ln^{4}(th(x))} + \frac{20log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))} - \frac{24sh^{2}(x)}{ln^{3}(th(x))}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数log_{th(x)}^{sh(ch(x))} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{th(x)}^{sh(ch(x))}\right)}{dx}\\=&(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})\\=&\frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{log_{th(x)}^{sh(ch(x))}th(x)}{ln(th(x))} - \frac{log_{th(x)}^{sh(ch(x))}}{ln(th(x))th(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{log_{th(x)}^{sh(ch(x))}th(x)}{ln(th(x))} - \frac{log_{th(x)}^{sh(ch(x))}}{ln(th(x))th(x)}\right)}{dx}\\=&\frac{-(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{2}(th(x))(th(x))sh(ch(x))} + \frac{-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{sh(x)sh(ch(x))sh(x)}{ln(th(x))sh(ch(x))} + \frac{(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th(x)}{ln(th(x))} + \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))th(x)}{ln^{2}(th(x))(th(x))} + \frac{log_{th(x)}^{sh(ch(x))}(1 - th^{2}(x))}{ln(th(x))} - \frac{(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln(th(x))th(x)} - \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))(th(x))th(x)} - \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln(th(x))th^{2}(x)}\\=&\frac{-2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} + \frac{2sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{sh^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{sh^{2}(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{2}(th(x))} + \frac{log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{2}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{2}(x)} - \frac{log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln(th(x))} - \frac{4log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} + \frac{2sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{sh^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{sh^{2}(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{2}(th(x))} + \frac{log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{2}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{2}(x)} - \frac{log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln(th(x))} - \frac{4log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))}\right)}{dx}\\=&\frac{-2*-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))th(x)} - \frac{2*-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} - \frac{2ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{2sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{2sh(x)ch(ch(x))*-(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{2*-2(1 - th^{2}(x))sh(x)ch(ch(x))th(x)}{ln^{3}(th(x))(th(x))sh(ch(x))} + \frac{2*-ch(ch(x))sh(x)sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{2ch(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh(x)sh(ch(x))sh(x)th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh(x)ch(ch(x))(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))} - \frac{-(1 - th^{2}(x))sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))(th(x))sh^{2}(ch(x))} - \frac{2sh(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{sh^{2}(x)*-2ch(ch(x))sh(x)ch^{2}(ch(x))}{ln(th(x))sh^{3}(ch(x))} - \frac{sh^{2}(x)*2ch(ch(x))sh(ch(x))sh(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{-(1 - th^{2}(x))ch(x)ch(ch(x))}{ln^{2}(th(x))(th(x))sh(ch(x))} + \frac{-ch(ch(x))sh(x)ch(x)ch(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{ch(x)sh(ch(x))sh(x)}{ln(th(x))sh(ch(x))} + \frac{-(1 - th^{2}(x))sh^{2}(x)}{ln^{2}(th(x))(th(x))} + \frac{2sh(x)ch(x)}{ln(th(x))} + \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{2}(x)}{ln^{2}(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))th^{2}(x)}{ln^{3}(th(x))(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}*2th(x)(1 - th^{2}(x))}{ln^{2}(th(x))} + \frac{(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln(th(x))th^{2}(x)} + \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))(th(x))th^{2}(x)} + \frac{log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln(th(x))th^{3}(x)} + \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{2}(th(x))th^{2}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{3}(th(x))(th(x))th^{2}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{2}(th(x))th^{3}(x)} - \frac{(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{2}(x)}{ln(th(x))} - \frac{log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))th^{2}(x)}{ln^{2}(th(x))(th(x))} - \frac{log_{th(x)}^{sh(ch(x))}*2th(x)(1 - th^{2}(x))}{ln(th(x))} - \frac{4(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{2}(th(x))} - \frac{4log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{3}(th(x))(th(x))}\\=&\frac{6sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{3sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{3ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{3sh^{2}(x)}{ln^{2}(th(x))th(x)} + \frac{6sh(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} - \frac{3sh^{2}(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3sh(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{2sh(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{3ch(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{3sh^{2}(x)th(x)}{ln^{2}(th(x))} - \frac{sh(x)ch^{2}(ch(x))ch(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh^{3}(x)ch^{3}(ch(x))}{ln(th(x))sh^{3}(ch(x))} - \frac{2sh^{3}(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{3sh(x)ch(x)}{ln(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th(x)} - \frac{18log_{th(x)}^{sh(ch(x))}th(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}th(x)}{ln^{2}(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln^{2}(th(x))} - \frac{12sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))} + \frac{18log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th(x)} - \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{3}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}}{ln(th(x))th(x)} - \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}th(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln(th(x))}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{6sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{3sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{3ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{3sh^{2}(x)}{ln^{2}(th(x))th(x)} + \frac{6sh(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} - \frac{3sh^{2}(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3sh(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{2sh(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{3ch(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{3sh^{2}(x)th(x)}{ln^{2}(th(x))} - \frac{sh(x)ch^{2}(ch(x))ch(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh^{3}(x)ch^{3}(ch(x))}{ln(th(x))sh^{3}(ch(x))} - \frac{2sh^{3}(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{sh(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{3sh(x)ch(x)}{ln(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th(x)} - \frac{18log_{th(x)}^{sh(ch(x))}th(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}th(x)}{ln^{2}(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln^{2}(th(x))} - \frac{12sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))} + \frac{18log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th(x)} - \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{3}(x)} + \frac{2log_{th(x)}^{sh(ch(x))}}{ln(th(x))th(x)} - \frac{6log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}th(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}th^{3}(x)}{ln(th(x))}\right)}{dx}\\=&\frac{6*-3(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{4}(th(x))(th(x))sh(ch(x))th^{2}(x)} + \frac{6*-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{3}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{6ch(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{6sh(x)sh(ch(x))sh(x)}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{6sh(x)ch(ch(x))*-2(1 - th^{2}(x))}{ln^{3}(th(x))sh(ch(x))th^{3}(x)} + \frac{3*-2(1 - th^{2}(x))sh^{2}(x)ch^{2}(ch(x))}{ln^{3}(th(x))(th(x))sh^{2}(ch(x))th(x)} + \frac{3*2sh(x)ch(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{3sh^{2}(x)*-2ch(ch(x))sh(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{3}(ch(x))th(x)} + \frac{3sh^{2}(x)*2ch(ch(x))sh(ch(x))sh(x)}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{3sh^{2}(x)ch^{2}(ch(x))*-(1 - th^{2}(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{2*-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))th^{2}(x)} + \frac{2ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{2sh(x)*-ch(ch(x))sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{2sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{2sh(x)ch(ch(x))*-2(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))th^{3}(x)} - \frac{3*-2(1 - th^{2}(x))ch(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))th(x)} - \frac{3*-ch(ch(x))sh(x)ch(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} - \frac{3sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{3ch(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{3ch(x)ch(ch(x))*-(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} - \frac{3*-2(1 - th^{2}(x))sh^{2}(x)}{ln^{3}(th(x))(th(x))th(x)} - \frac{3*2sh(x)ch(x)}{ln^{2}(th(x))th(x)} - \frac{3sh^{2}(x)*-(1 - th^{2}(x))}{ln^{2}(th(x))th^{2}(x)} + \frac{6*-3(1 - th^{2}(x))sh(x)ch(ch(x))th^{2}(x)}{ln^{4}(th(x))(th(x))sh(ch(x))} + \frac{6*-ch(ch(x))sh(x)sh(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh^{2}(ch(x))} + \frac{6ch(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{6sh(x)sh(ch(x))sh(x)th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{6sh(x)ch(ch(x))*2th(x)(1 - th^{2}(x))}{ln^{3}(th(x))sh(ch(x))} - \frac{3*-2(1 - th^{2}(x))sh^{2}(x)ch^{2}(ch(x))th(x)}{ln^{3}(th(x))(th(x))sh^{2}(ch(x))} - \frac{3*2sh(x)ch(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3sh^{2}(x)*-2ch(ch(x))sh(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{3}(ch(x))} - \frac{3sh^{2}(x)*2ch(ch(x))sh(ch(x))sh(x)th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3sh^{2}(x)ch^{2}(ch(x))(1 - th^{2}(x))}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3*-2(1 - th^{2}(x))sh(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))(th(x))sh(ch(x))} - \frac{3*-ch(ch(x))sh(x)sh(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3ch(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{3sh(x)sh(ch(x))sh(x)th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{3sh(x)ch(ch(x))*2th(x)(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))} - \frac{2*-(1 - th^{2}(x))sh(x)ch(x)ch^{2}(ch(x))}{ln^{2}(th(x))(th(x))sh^{2}(ch(x))} - \frac{2ch(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{2sh(x)*-2ch(ch(x))sh(x)ch(x)ch^{2}(ch(x))}{ln(th(x))sh^{3}(ch(x))} - \frac{2sh(x)sh(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{2sh(x)ch(x)*2ch(ch(x))sh(ch(x))sh(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{3*-2(1 - th^{2}(x))ch(x)ch(ch(x))th(x)}{ln^{3}(th(x))(th(x))sh(ch(x))} + \frac{3*-ch(ch(x))sh(x)ch(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{3sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{3ch(x)sh(ch(x))sh(x)th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{3ch(x)ch(ch(x))(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{3*-2(1 - th^{2}(x))sh^{2}(x)th(x)}{ln^{3}(th(x))(th(x))} + \frac{3*2sh(x)ch(x)th(x)}{ln^{2}(th(x))} + \frac{3sh^{2}(x)(1 - th^{2}(x))}{ln^{2}(th(x))} - \frac{-(1 - th^{2}(x))sh(x)ch^{2}(ch(x))ch(x)}{ln^{2}(th(x))(th(x))sh^{2}(ch(x))} - \frac{ch(x)ch^{2}(ch(x))ch(x)}{ln(th(x))sh^{2}(ch(x))} - \frac{sh(x)*-2ch(ch(x))sh(x)ch^{2}(ch(x))ch(x)}{ln(th(x))sh^{3}(ch(x))} - \frac{sh(x)*2ch(ch(x))sh(ch(x))sh(x)ch(x)}{ln(th(x))sh^{2}(ch(x))} - \frac{sh(x)ch^{2}(ch(x))sh(x)}{ln(th(x))sh^{2}(ch(x))} + \frac{-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))th^{2}(x)} + \frac{-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{sh(x)ch(ch(x))*-2(1 - th^{2}(x))}{ln^{2}(th(x))sh(ch(x))th^{3}(x)} - \frac{2*-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))} - \frac{2*-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{2ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} - \frac{2sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{2*-(1 - th^{2}(x))sh^{3}(x)ch^{3}(ch(x))}{ln^{2}(th(x))(th(x))sh^{3}(ch(x))} + \frac{2*-3ch(ch(x))sh(x)sh^{3}(x)ch^{3}(ch(x))}{ln(th(x))sh^{4}(ch(x))} + \frac{2*3sh^{2}(x)ch(x)ch^{3}(ch(x))}{ln(th(x))sh^{3}(ch(x))} + \frac{2sh^{3}(x)*3ch^{2}(ch(x))sh(ch(x))sh(x)}{ln(th(x))sh^{3}(ch(x))} - \frac{2*-(1 - th^{2}(x))sh^{3}(x)ch(ch(x))}{ln^{2}(th(x))(th(x))sh(ch(x))} - \frac{2*-ch(ch(x))sh(x)sh^{3}(x)ch(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{2*3sh^{2}(x)ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} - \frac{2sh^{3}(x)sh(ch(x))sh(x)}{ln(th(x))sh(ch(x))} + \frac{2*-2(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{3}(th(x))(th(x))sh(ch(x))} + \frac{2ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} + \frac{2sh(x)*-ch(ch(x))sh(x)ch(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{2sh(x)sh(ch(x))sh(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{-(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{2}(th(x))(th(x))sh(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} + \frac{sh(x)*-ch(ch(x))sh(x)ch(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{sh(x)sh(ch(x))sh(x)}{ln(th(x))sh(ch(x))} + \frac{3*-(1 - th^{2}(x))sh(x)ch(x)}{ln^{2}(th(x))(th(x))} + \frac{3ch(x)ch(x)}{ln(th(x))} + \frac{3sh(x)sh(x)}{ln(th(x))} + \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{3}(x)}{ln^{3}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))th^{3}(x)}{ln^{4}(th(x))(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}*3th^{2}(x)(1 - th^{2}(x))}{ln^{3}(th(x))} + \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{2}(th(x))th(x)} + \frac{6log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{3}(th(x))(th(x))th(x)} + \frac{6log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))th^{2}(x)} - \frac{18(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th(x)}{ln^{3}(th(x))} - \frac{18log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))th(x)}{ln^{4}(th(x))(th(x))} - \frac{18log_{th(x)}^{sh(ch(x))}(1 - th^{2}(x))}{ln^{3}(th(x))} + \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th(x)}{ln^{2}(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))th(x)}{ln^{3}(th(x))(th(x))} + \frac{6log_{th(x)}^{sh(ch(x))}(1 - th^{2}(x))}{ln^{2}(th(x))} - \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{3}(x)}{ln^{2}(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))th^{3}(x)}{ln^{3}(th(x))(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}*3th^{2}(x)(1 - th^{2}(x))}{ln^{2}(th(x))} - \frac{12*-3(1 - th^{2}(x))sh(x)ch(ch(x))}{ln^{4}(th(x))(th(x))sh(ch(x))} - \frac{12*-ch(ch(x))sh(x)sh(x)ch(ch(x))}{ln^{3}(th(x))sh^{2}(ch(x))} - \frac{12ch(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))} - \frac{12sh(x)sh(ch(x))sh(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{18(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{3}(th(x))th(x)} + \frac{18log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln^{4}(th(x))(th(x))th(x)} + \frac{18log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{3}(th(x))th^{2}(x)} - \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{2}(th(x))th^{3}(x)} - \frac{6log_{th(x)}^{sh(ch(x))}*-2(1 - th^{2}(x))}{ln^{3}(th(x))(th(x))th^{3}(x)} - \frac{6log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln^{2}(th(x))th^{4}(x)} - \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))(th(x))th^{3}(x)} - \frac{2log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln(th(x))th^{4}(x)} + \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln(th(x))th(x)} + \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln^{2}(th(x))(th(x))th(x)} + \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))}{ln(th(x))th^{2}(x)} - \frac{6(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})}{ln^{3}(th(x))th^{3}(x)} - \frac{6log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln^{4}(th(x))(th(x))th^{3}(x)} - \frac{6log_{th(x)}^{sh(ch(x))}*-3(1 - th^{2}(x))}{ln^{3}(th(x))th^{4}(x)} - \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th(x)}{ln(th(x))} - \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))th(x)}{ln^{2}(th(x))(th(x))} - \frac{2log_{th(x)}^{sh(ch(x))}(1 - th^{2}(x))}{ln(th(x))} + \frac{2(\frac{(\frac{(ch(ch(x))sh(x))}{(sh(ch(x)))} - \frac{((1 - th^{2}(x)))log_{th(x)}^{sh(ch(x))}}{(th(x))})}{(ln(th(x)))})th^{3}(x)}{ln(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}*-(1 - th^{2}(x))th^{3}(x)}{ln^{2}(th(x))(th(x))} + \frac{2log_{th(x)}^{sh(ch(x))}*3th^{2}(x)(1 - th^{2}(x))}{ln(th(x))}\\=&\frac{-24sh(x)ch(ch(x))}{ln^{4}(th(x))sh(ch(x))th^{3}(x)} + \frac{72sh(x)ch(ch(x))}{ln^{4}(th(x))sh(ch(x))th(x)} - \frac{12sh^{2}(x)ch^{2}(ch(x))}{ln^{3}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{3ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{12sh^{2}(x)}{ln^{3}(th(x))th^{2}(x)} - \frac{16sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{3}(x)} + \frac{24sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th(x)} + \frac{8sh(x)ch(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} - \frac{8sh^{3}(x)ch^{3}(ch(x))}{ln^{2}(th(x))sh^{3}(ch(x))th(x)} + \frac{8sh^{3}(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} - \frac{5sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} - \frac{6sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{3}(x)} + \frac{4sh(x)ch^{2}(ch(x))ch(x)}{ln^{2}(th(x))sh^{2}(ch(x))th(x)} + \frac{12ch(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{2}(x)} + \frac{6sh^{2}(x)}{ln^{2}(th(x))th^{2}(x)} - \frac{24sh(x)ch(ch(x))th^{3}(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{3ch(ch(x))ch(x)}{ln^{2}(th(x))sh(ch(x))th^{2}(x)} + \frac{12ch(x)ch(ch(x))th^{2}(x)}{ln^{3}(th(x))sh(ch(x))} - \frac{72sh(x)ch(ch(x))th(x)}{ln^{4}(th(x))sh(ch(x))} + \frac{24sh(x)ch(ch(x))th^{3}(x)}{ln^{4}(th(x))sh(ch(x))} - \frac{12sh(x)ch(x)}{ln^{2}(th(x))th(x)} - \frac{6ch(x)ch(ch(x))th^{2}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{12sh^{2}(x)ch^{2}(ch(x))th^{2}(x)}{ln^{3}(th(x))sh^{2}(ch(x))} + \frac{16sh(x)ch(ch(x))th(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{8sh(x)ch(ch(x))th^{3}(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{24ch(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))} + \frac{12sh^{2}(x)th^{2}(x)}{ln^{3}(th(x))} - \frac{8sh(x)ch(x)ch^{2}(ch(x))th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{8sh^{3}(x)ch^{3}(ch(x))th(x)}{ln^{2}(th(x))sh^{3}(ch(x))} - \frac{8sh^{3}(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{2sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{4sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th(x)} + \frac{8sh(x)ch(ch(x))th(x)}{ln^{3}(th(x))sh(ch(x))} + \frac{6sh^{2}(x)ch^{2}(ch(x))th^{2}(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{2sh(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))th^{3}(x)} - \frac{4sh(x)ch^{2}(ch(x))ch(x)th(x)}{ln^{2}(th(x))sh^{2}(ch(x))} - \frac{3ch(x)ch(ch(x))}{ln^{2}(th(x))sh(ch(x))} - \frac{6sh^{2}(x)th^{2}(x)}{ln^{2}(th(x))} - \frac{6sh^{2}(x)ch(ch(x))ch(x)}{ln(th(x))sh(ch(x))} - \frac{3ch^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} + \frac{6sh^{2}(x)ch^{3}(ch(x))ch(x)}{ln(th(x))sh^{3}(ch(x))} - \frac{8sh(x)ch(ch(x))}{ln^{3}(th(x))sh(ch(x))th^{3}(x)} - \frac{sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))th^{2}(x)} + \frac{6sh^{2}(x)ch(x)ch^{3}(ch(x))}{ln(th(x))sh^{3}(ch(x))} + \frac{12sh(x)ch(x)th(x)}{ln^{2}(th(x))} + \frac{3ch(ch(x))ch(x)}{ln^{2}(th(x))sh(ch(x))} - \frac{6sh^{2}(x)ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} - \frac{2sh(x)ch(ch(x))th(x)}{ln^{2}(th(x))sh(ch(x))} + \frac{5sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{8sh^{4}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{6sh^{4}(x)ch^{4}(ch(x))}{ln(th(x))sh^{4}(ch(x))} + \frac{24sh^{2}(x)ch^{2}(ch(x))}{ln^{3}(th(x))sh^{2}(ch(x))} - \frac{5sh^{2}(x)ch^{2}(ch(x))}{ln^{2}(th(x))sh^{2}(ch(x))} + \frac{ch(x)ch(ch(x))}{ln(th(x))sh(ch(x))} - \frac{sh^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{3sh^{2}(x)ch^{2}(ch(x))}{ln(th(x))sh^{2}(ch(x))} - \frac{2sh^{4}(x)}{ln(th(x))} + \frac{4sh^{2}(x)}{ln(th(x))} + \frac{3ch^{2}(x)}{ln(th(x))} + \frac{24log_{th(x)}^{sh(ch(x))}th^{4}(x)}{ln^{4}(th(x))} - \frac{96log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{4}(th(x))} + \frac{72log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{3}(th(x))} - \frac{36log_{th(x)}^{sh(ch(x))}th^{4}(x)}{ln^{3}(th(x))} - \frac{72log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th^{2}(x)} - \frac{32log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{2}(x)} - \frac{32log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln^{2}(th(x))} + \frac{22log_{th(x)}^{sh(ch(x))}th^{4}(x)}{ln^{2}(th(x))} + \frac{22log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))th^{4}(x)} - \frac{96log_{th(x)}^{sh(ch(x))}}{ln^{4}(th(x))th^{2}(x)} + \frac{6log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{4}(x)} - \frac{8log_{th(x)}^{sh(ch(x))}}{ln(th(x))th^{2}(x)} + \frac{36log_{th(x)}^{sh(ch(x))}}{ln^{3}(th(x))th^{4}(x)} + \frac{8log_{th(x)}^{sh(ch(x))}th^{2}(x)}{ln(th(x))} - \frac{6log_{th(x)}^{sh(ch(x))}th^{4}(x)}{ln(th(x))} + \frac{24log_{th(x)}^{sh(ch(x))}}{ln^{4}(th(x))th^{4}(x)} + \frac{144log_{th(x)}^{sh(ch(x))}}{ln^{4}(th(x))} + \frac{20log_{th(x)}^{sh(ch(x))}}{ln^{2}(th(x))} - \frac{24sh^{2}(x)}{ln^{3}(th(x))}\\ \end{split}\end{equation} \]
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