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。
\[ \begin{equation}\begin{split}【1/1】求函数lg(log_{sin(x)}^{sinh(x)}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(log_{sin(x)}^{sinh(x)})\right)}{dx}\\=&\frac{(\frac{(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{(ln(sin(x)))})}{ln{10}(log_{sin(x)}^{sinh(x)})}\\=&\frac{cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{cos(x)}{ln(sin(x))ln{10}sin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{cos(x)}{ln(sin(x))ln{10}sin(x)}\right)}{dx}\\=&\frac{(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})cosh(x)}{ln(sin(x))ln{10}sinh(x)} + \frac{-cos(x)cosh(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}sinh(x)} + \frac{-0cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}sinh(x)} + \frac{-cosh(x)cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} + \frac{sinh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{-cos(x)cos(x)}{ln^{2}(sin(x))(sin(x))ln{10}sin(x)} - \frac{-0cos(x)}{ln(sin(x))ln^{2}{10}sin(x)} - \frac{-cos(x)cos(x)}{ln(sin(x))ln{10}sin^{2}(x)} - \frac{-sin(x)}{ln(sin(x))ln{10}sin(x)}\\=&\frac{-cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} + \frac{1}{log(sin(x), sinh(x))ln(sin(x))ln{10}} + \frac{cos^{2}(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} + \frac{cos^{2}(x)}{ln(sin(x))ln{10}sin^{2}(x)} + \frac{1}{ln(sin(x))ln{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} + \frac{1}{log(sin(x), sinh(x))ln(sin(x))ln{10}} + \frac{cos^{2}(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} + \frac{cos^{2}(x)}{ln(sin(x))ln{10}sin^{2}(x)} + \frac{1}{ln(sin(x))ln{10}}\right)}{dx}\\=&\frac{-(\frac{-2(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{3}(ln(sin(x)))})cosh^{2}(x)}{ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{-2cos(x)cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{3}(sin(x))(sin(x))ln{10}sinh^{2}(x)} - \frac{-0cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln^{2}{10}sinh^{2}(x)} - \frac{-2cosh(x)cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{3}(x)} - \frac{2cosh(x)sinh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})cosh^{2}(x)}{ln(sin(x))ln{10}sinh^{2}(x)} - \frac{-cos(x)cosh^{2}(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}sinh^{2}(x)} - \frac{-0cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}sinh^{2}(x)} - \frac{-2cosh(x)cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{3}(x)} - \frac{2cosh(x)sinh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} + \frac{(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})}{ln(sin(x))ln{10}} + \frac{-cos(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}} + \frac{-0}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}} + \frac{-2cos(x)cos^{2}(x)}{ln^{3}(sin(x))(sin(x))ln{10}sin^{2}(x)} + \frac{-0cos^{2}(x)}{ln^{2}(sin(x))ln^{2}{10}sin^{2}(x)} + \frac{-2cos(x)cos^{2}(x)}{ln^{2}(sin(x))ln{10}sin^{3}(x)} + \frac{-2cos(x)sin(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} + \frac{-cos(x)cos^{2}(x)}{ln^{2}(sin(x))(sin(x))ln{10}sin^{2}(x)} + \frac{-0cos^{2}(x)}{ln(sin(x))ln^{2}{10}sin^{2}(x)} + \frac{-2cos(x)cos^{2}(x)}{ln(sin(x))ln{10}sin^{3}(x)} + \frac{-2cos(x)sin(x)}{ln(sin(x))ln{10}sin^{2}(x)} + \frac{-cos(x)}{ln^{2}(sin(x))(sin(x))ln{10}} + \frac{-0}{ln(sin(x))ln^{2}{10}}\\=&\frac{2cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{3}(x)} + \frac{3cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{3}(x)} - \frac{3cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh(x)} + \frac{2cosh^{3}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{3}(x)} - \frac{2cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{2cos^{3}(x)}{ln^{3}(sin(x))ln{10}sin^{3}(x)} - \frac{3cos^{3}(x)}{ln^{2}(sin(x))ln{10}sin^{3}(x)} - \frac{2cos^{3}(x)}{ln(sin(x))ln{10}sin^{3}(x)} - \frac{3cos(x)}{ln^{2}(sin(x))ln{10}sin(x)} - \frac{2cos(x)}{ln(sin(x))ln{10}sin(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{3}(x)} + \frac{3cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{3}(x)} - \frac{3cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh(x)} + \frac{2cosh^{3}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{3}(x)} - \frac{2cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{2cos^{3}(x)}{ln^{3}(sin(x))ln{10}sin^{3}(x)} - \frac{3cos^{3}(x)}{ln^{2}(sin(x))ln{10}sin^{3}(x)} - \frac{2cos^{3}(x)}{ln(sin(x))ln{10}sin^{3}(x)} - \frac{3cos(x)}{ln^{2}(sin(x))ln{10}sin(x)} - \frac{2cos(x)}{ln(sin(x))ln{10}sin(x)}\right)}{dx}\\=&\frac{2(\frac{-3(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{4}(ln(sin(x)))})cosh^{3}(x)}{ln^{3}(sin(x))ln{10}sinh^{3}(x)} + \frac{2*-3cos(x)cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{4}(sin(x))(sin(x))ln{10}sinh^{3}(x)} + \frac{2*-0cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln^{2}{10}sinh^{3}(x)} + \frac{2*-3cosh(x)cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{4}(x)} + \frac{2*3cosh^{2}(x)sinh(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{3}(x)} + \frac{3(\frac{-2(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{3}(ln(sin(x)))})cosh^{3}(x)}{ln^{2}(sin(x))ln{10}sinh^{3}(x)} + \frac{3*-2cos(x)cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{3}(sin(x))(sin(x))ln{10}sinh^{3}(x)} + \frac{3*-0cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln^{2}{10}sinh^{3}(x)} + \frac{3*-3cosh(x)cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{4}(x)} + \frac{3*3cosh^{2}(x)sinh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{3}(x)} - \frac{3(\frac{-2(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{3}(ln(sin(x)))})cosh(x)}{ln^{2}(sin(x))ln{10}sinh(x)} - \frac{3*-2cos(x)cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{3}(sin(x))(sin(x))ln{10}sinh(x)} - \frac{3*-0cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln^{2}{10}sinh(x)} - \frac{3*-cosh(x)cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{3sinh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh(x)} + \frac{2(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})cosh^{3}(x)}{ln(sin(x))ln{10}sinh^{3}(x)} + \frac{2*-cos(x)cosh^{3}(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}sinh^{3}(x)} + \frac{2*-0cosh^{3}(x)}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}sinh^{3}(x)} + \frac{2*-3cosh(x)cosh^{3}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{4}(x)} + \frac{2*3cosh^{2}(x)sinh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{3}(x)} - \frac{2(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})cosh(x)}{ln(sin(x))ln{10}sinh(x)} - \frac{2*-cos(x)cosh(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}sinh(x)} - \frac{2*-0cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}sinh(x)} - \frac{2*-cosh(x)cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} - \frac{2sinh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{2*-3cos(x)cos^{3}(x)}{ln^{4}(sin(x))(sin(x))ln{10}sin^{3}(x)} - \frac{2*-0cos^{3}(x)}{ln^{3}(sin(x))ln^{2}{10}sin^{3}(x)} - \frac{2*-3cos(x)cos^{3}(x)}{ln^{3}(sin(x))ln{10}sin^{4}(x)} - \frac{2*-3cos^{2}(x)sin(x)}{ln^{3}(sin(x))ln{10}sin^{3}(x)} - \frac{3*-2cos(x)cos^{3}(x)}{ln^{3}(sin(x))(sin(x))ln{10}sin^{3}(x)} - \frac{3*-0cos^{3}(x)}{ln^{2}(sin(x))ln^{2}{10}sin^{3}(x)} - \frac{3*-3cos(x)cos^{3}(x)}{ln^{2}(sin(x))ln{10}sin^{4}(x)} - \frac{3*-3cos^{2}(x)sin(x)}{ln^{2}(sin(x))ln{10}sin^{3}(x)} - \frac{2*-cos(x)cos^{3}(x)}{ln^{2}(sin(x))(sin(x))ln{10}sin^{3}(x)} - \frac{2*-0cos^{3}(x)}{ln(sin(x))ln^{2}{10}sin^{3}(x)} - \frac{2*-3cos(x)cos^{3}(x)}{ln(sin(x))ln{10}sin^{4}(x)} - \frac{2*-3cos^{2}(x)sin(x)}{ln(sin(x))ln{10}sin^{3}(x)} - \frac{3*-2cos(x)cos(x)}{ln^{3}(sin(x))(sin(x))ln{10}sin(x)} - \frac{3*-0cos(x)}{ln^{2}(sin(x))ln^{2}{10}sin(x)} - \frac{3*-cos(x)cos(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} - \frac{3*-sin(x)}{ln^{2}(sin(x))ln{10}sin(x)} - \frac{2*-cos(x)cos(x)}{ln^{2}(sin(x))(sin(x))ln{10}sin(x)} - \frac{2*-0cos(x)}{ln(sin(x))ln^{2}{10}sin(x)} - \frac{2*-cos(x)cos(x)}{ln(sin(x))ln{10}sin^{2}(x)} - \frac{2*-sin(x)}{ln(sin(x))ln{10}sin(x)}\\=&\frac{-6cosh^{4}(x)}{{\left(log(sin(x), sinh(x))^{4}ln^{4}(sin(x))ln{10}sinh^{4}(x)} - \frac{12cosh^{4}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{4}(x)} + \frac{12cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{2}(x)} - \frac{11cosh^{4}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{4}(x)} + \frac{14cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{6cosh^{4}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{4}(x)} + \frac{8cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} - \frac{3}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}} - \frac{2}{log(sin(x), sinh(x))ln(sin(x))ln{10}} + \frac{6cos^{4}(x)}{ln^{4}(sin(x))ln{10}sin^{4}(x)} + \frac{12cos^{4}(x)}{ln^{3}(sin(x))ln{10}sin^{4}(x)} + \frac{11cos^{4}(x)}{ln^{2}(sin(x))ln{10}sin^{4}(x)} + \frac{12cos^{2}(x)}{ln^{3}(sin(x))ln{10}sin^{2}(x)} + \frac{6cos^{4}(x)}{ln(sin(x))ln{10}sin^{4}(x)} + \frac{14cos^{2}(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} + \frac{8cos^{2}(x)}{ln(sin(x))ln{10}sin^{2}(x)} + \frac{3}{ln^{2}(sin(x))ln{10}} + \frac{2}{ln(sin(x))ln{10}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数lg(log_{sin(x)}^{sinh(x)}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(log_{sin(x)}^{sinh(x)})\right)}{dx}\\=&\frac{(\frac{(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{(ln(sin(x)))})}{ln{10}(log_{sin(x)}^{sinh(x)})}\\=&\frac{cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{cos(x)}{ln(sin(x))ln{10}sin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{cos(x)}{ln(sin(x))ln{10}sin(x)}\right)}{dx}\\=&\frac{(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})cosh(x)}{ln(sin(x))ln{10}sinh(x)} + \frac{-cos(x)cosh(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}sinh(x)} + \frac{-0cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}sinh(x)} + \frac{-cosh(x)cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} + \frac{sinh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{-cos(x)cos(x)}{ln^{2}(sin(x))(sin(x))ln{10}sin(x)} - \frac{-0cos(x)}{ln(sin(x))ln^{2}{10}sin(x)} - \frac{-cos(x)cos(x)}{ln(sin(x))ln{10}sin^{2}(x)} - \frac{-sin(x)}{ln(sin(x))ln{10}sin(x)}\\=&\frac{-cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} + \frac{1}{log(sin(x), sinh(x))ln(sin(x))ln{10}} + \frac{cos^{2}(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} + \frac{cos^{2}(x)}{ln(sin(x))ln{10}sin^{2}(x)} + \frac{1}{ln(sin(x))ln{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} + \frac{1}{log(sin(x), sinh(x))ln(sin(x))ln{10}} + \frac{cos^{2}(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} + \frac{cos^{2}(x)}{ln(sin(x))ln{10}sin^{2}(x)} + \frac{1}{ln(sin(x))ln{10}}\right)}{dx}\\=&\frac{-(\frac{-2(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{3}(ln(sin(x)))})cosh^{2}(x)}{ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{-2cos(x)cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{3}(sin(x))(sin(x))ln{10}sinh^{2}(x)} - \frac{-0cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln^{2}{10}sinh^{2}(x)} - \frac{-2cosh(x)cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{3}(x)} - \frac{2cosh(x)sinh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})cosh^{2}(x)}{ln(sin(x))ln{10}sinh^{2}(x)} - \frac{-cos(x)cosh^{2}(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}sinh^{2}(x)} - \frac{-0cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}sinh^{2}(x)} - \frac{-2cosh(x)cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{3}(x)} - \frac{2cosh(x)sinh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} + \frac{(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})}{ln(sin(x))ln{10}} + \frac{-cos(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}} + \frac{-0}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}} + \frac{-2cos(x)cos^{2}(x)}{ln^{3}(sin(x))(sin(x))ln{10}sin^{2}(x)} + \frac{-0cos^{2}(x)}{ln^{2}(sin(x))ln^{2}{10}sin^{2}(x)} + \frac{-2cos(x)cos^{2}(x)}{ln^{2}(sin(x))ln{10}sin^{3}(x)} + \frac{-2cos(x)sin(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} + \frac{-cos(x)cos^{2}(x)}{ln^{2}(sin(x))(sin(x))ln{10}sin^{2}(x)} + \frac{-0cos^{2}(x)}{ln(sin(x))ln^{2}{10}sin^{2}(x)} + \frac{-2cos(x)cos^{2}(x)}{ln(sin(x))ln{10}sin^{3}(x)} + \frac{-2cos(x)sin(x)}{ln(sin(x))ln{10}sin^{2}(x)} + \frac{-cos(x)}{ln^{2}(sin(x))(sin(x))ln{10}} + \frac{-0}{ln(sin(x))ln^{2}{10}}\\=&\frac{2cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{3}(x)} + \frac{3cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{3}(x)} - \frac{3cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh(x)} + \frac{2cosh^{3}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{3}(x)} - \frac{2cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{2cos^{3}(x)}{ln^{3}(sin(x))ln{10}sin^{3}(x)} - \frac{3cos^{3}(x)}{ln^{2}(sin(x))ln{10}sin^{3}(x)} - \frac{2cos^{3}(x)}{ln(sin(x))ln{10}sin^{3}(x)} - \frac{3cos(x)}{ln^{2}(sin(x))ln{10}sin(x)} - \frac{2cos(x)}{ln(sin(x))ln{10}sin(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{3}(x)} + \frac{3cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{3}(x)} - \frac{3cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh(x)} + \frac{2cosh^{3}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{3}(x)} - \frac{2cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{2cos^{3}(x)}{ln^{3}(sin(x))ln{10}sin^{3}(x)} - \frac{3cos^{3}(x)}{ln^{2}(sin(x))ln{10}sin^{3}(x)} - \frac{2cos^{3}(x)}{ln(sin(x))ln{10}sin^{3}(x)} - \frac{3cos(x)}{ln^{2}(sin(x))ln{10}sin(x)} - \frac{2cos(x)}{ln(sin(x))ln{10}sin(x)}\right)}{dx}\\=&\frac{2(\frac{-3(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{4}(ln(sin(x)))})cosh^{3}(x)}{ln^{3}(sin(x))ln{10}sinh^{3}(x)} + \frac{2*-3cos(x)cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{4}(sin(x))(sin(x))ln{10}sinh^{3}(x)} + \frac{2*-0cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln^{2}{10}sinh^{3}(x)} + \frac{2*-3cosh(x)cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{4}(x)} + \frac{2*3cosh^{2}(x)sinh(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{3}(x)} + \frac{3(\frac{-2(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{3}(ln(sin(x)))})cosh^{3}(x)}{ln^{2}(sin(x))ln{10}sinh^{3}(x)} + \frac{3*-2cos(x)cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{3}(sin(x))(sin(x))ln{10}sinh^{3}(x)} + \frac{3*-0cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln^{2}{10}sinh^{3}(x)} + \frac{3*-3cosh(x)cosh^{3}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{4}(x)} + \frac{3*3cosh^{2}(x)sinh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{3}(x)} - \frac{3(\frac{-2(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{3}(ln(sin(x)))})cosh(x)}{ln^{2}(sin(x))ln{10}sinh(x)} - \frac{3*-2cos(x)cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{3}(sin(x))(sin(x))ln{10}sinh(x)} - \frac{3*-0cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln^{2}{10}sinh(x)} - \frac{3*-cosh(x)cosh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{3sinh(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh(x)} + \frac{2(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})cosh^{3}(x)}{ln(sin(x))ln{10}sinh^{3}(x)} + \frac{2*-cos(x)cosh^{3}(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}sinh^{3}(x)} + \frac{2*-0cosh^{3}(x)}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}sinh^{3}(x)} + \frac{2*-3cosh(x)cosh^{3}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{4}(x)} + \frac{2*3cosh^{2}(x)sinh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{3}(x)} - \frac{2(\frac{-(\frac{(cosh(x))}{(sinh(x))} - \frac{(cos(x))log_{sin(x)}^{sinh(x)}}{(sin(x))})}{{\left(log(sin(x), sinh(x))^{2}(ln(sin(x)))})cosh(x)}{ln(sin(x))ln{10}sinh(x)} - \frac{2*-cos(x)cosh(x)}{log(sin(x), sinh(x))ln^{2}(sin(x))(sin(x))ln{10}sinh(x)} - \frac{2*-0cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln^{2}{10}sinh(x)} - \frac{2*-cosh(x)cosh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} - \frac{2sinh(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh(x)} - \frac{2*-3cos(x)cos^{3}(x)}{ln^{4}(sin(x))(sin(x))ln{10}sin^{3}(x)} - \frac{2*-0cos^{3}(x)}{ln^{3}(sin(x))ln^{2}{10}sin^{3}(x)} - \frac{2*-3cos(x)cos^{3}(x)}{ln^{3}(sin(x))ln{10}sin^{4}(x)} - \frac{2*-3cos^{2}(x)sin(x)}{ln^{3}(sin(x))ln{10}sin^{3}(x)} - \frac{3*-2cos(x)cos^{3}(x)}{ln^{3}(sin(x))(sin(x))ln{10}sin^{3}(x)} - \frac{3*-0cos^{3}(x)}{ln^{2}(sin(x))ln^{2}{10}sin^{3}(x)} - \frac{3*-3cos(x)cos^{3}(x)}{ln^{2}(sin(x))ln{10}sin^{4}(x)} - \frac{3*-3cos^{2}(x)sin(x)}{ln^{2}(sin(x))ln{10}sin^{3}(x)} - \frac{2*-cos(x)cos^{3}(x)}{ln^{2}(sin(x))(sin(x))ln{10}sin^{3}(x)} - \frac{2*-0cos^{3}(x)}{ln(sin(x))ln^{2}{10}sin^{3}(x)} - \frac{2*-3cos(x)cos^{3}(x)}{ln(sin(x))ln{10}sin^{4}(x)} - \frac{2*-3cos^{2}(x)sin(x)}{ln(sin(x))ln{10}sin^{3}(x)} - \frac{3*-2cos(x)cos(x)}{ln^{3}(sin(x))(sin(x))ln{10}sin(x)} - \frac{3*-0cos(x)}{ln^{2}(sin(x))ln^{2}{10}sin(x)} - \frac{3*-cos(x)cos(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} - \frac{3*-sin(x)}{ln^{2}(sin(x))ln{10}sin(x)} - \frac{2*-cos(x)cos(x)}{ln^{2}(sin(x))(sin(x))ln{10}sin(x)} - \frac{2*-0cos(x)}{ln(sin(x))ln^{2}{10}sin(x)} - \frac{2*-cos(x)cos(x)}{ln(sin(x))ln{10}sin^{2}(x)} - \frac{2*-sin(x)}{ln(sin(x))ln{10}sin(x)}\\=&\frac{-6cosh^{4}(x)}{{\left(log(sin(x), sinh(x))^{4}ln^{4}(sin(x))ln{10}sinh^{4}(x)} - \frac{12cosh^{4}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{4}(x)} + \frac{12cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{3}ln^{3}(sin(x))ln{10}sinh^{2}(x)} - \frac{11cosh^{4}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{4}(x)} + \frac{14cosh^{2}(x)}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}sinh^{2}(x)} - \frac{6cosh^{4}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{4}(x)} + \frac{8cosh^{2}(x)}{log(sin(x), sinh(x))ln(sin(x))ln{10}sinh^{2}(x)} - \frac{3}{{\left(log(sin(x), sinh(x))^{2}ln^{2}(sin(x))ln{10}} - \frac{2}{log(sin(x), sinh(x))ln(sin(x))ln{10}} + \frac{6cos^{4}(x)}{ln^{4}(sin(x))ln{10}sin^{4}(x)} + \frac{12cos^{4}(x)}{ln^{3}(sin(x))ln{10}sin^{4}(x)} + \frac{11cos^{4}(x)}{ln^{2}(sin(x))ln{10}sin^{4}(x)} + \frac{12cos^{2}(x)}{ln^{3}(sin(x))ln{10}sin^{2}(x)} + \frac{6cos^{4}(x)}{ln(sin(x))ln{10}sin^{4}(x)} + \frac{14cos^{2}(x)}{ln^{2}(sin(x))ln{10}sin^{2}(x)} + \frac{8cos^{2}(x)}{ln(sin(x))ln{10}sin^{2}(x)} + \frac{3}{ln^{2}(sin(x))ln{10}} + \frac{2}{ln(sin(x))ln{10}}\\ \end{split}\end{equation} \]
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