本次共计算 4 个题目：每一题对 x 求 4 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/4】求函数arcsin(sinh(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arcsin(sinh(x))\right)}{dx}\\=&(\frac{(cosh(x))}{((1 - (sinh(x))^{2})^{\frac{1}{2}})})\\=&\frac{cosh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{cosh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-2sinh(x)cosh(x) + 0)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}})cosh(x) + \frac{sinh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\\=&\frac{sinh(x)cosh^{2}(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sinh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{sinh(x)cosh^{2}(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sinh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-2sinh(x)cosh(x) + 0)}{(-sinh^{2}(x) + 1)^{\frac{5}{2}}})sinh(x)cosh^{2}(x) + \frac{cosh(x)cosh^{2}(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sinh(x)*2cosh(x)sinh(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + (\frac{\frac{-1}{2}(-2sinh(x)cosh(x) + 0)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}})sinh(x) + \frac{cosh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\\=&\frac{3sinh^{2}(x)cosh^{3}(x)}{(-sinh^{2}(x) + 1)^{\frac{5}{2}}} + \frac{cosh^{3}(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{3sinh^{2}(x)cosh(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{cosh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3sinh^{2}(x)cosh^{3}(x)}{(-sinh^{2}(x) + 1)^{\frac{5}{2}}} + \frac{cosh^{3}(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{3sinh^{2}(x)cosh(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{cosh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-2sinh(x)cosh(x) + 0)}{(-sinh^{2}(x) + 1)^{\frac{7}{2}}})sinh^{2}(x)cosh^{3}(x) + \frac{3*2sinh(x)cosh(x)cosh^{3}(x)}{(-sinh^{2}(x) + 1)^{\frac{5}{2}}} + \frac{3sinh^{2}(x)*3cosh^{2}(x)sinh(x)}{(-sinh^{2}(x) + 1)^{\frac{5}{2}}} + (\frac{\frac{-3}{2}(-2sinh(x)cosh(x) + 0)}{(-sinh^{2}(x) + 1)^{\frac{5}{2}}})cosh^{3}(x) + \frac{3cosh^{2}(x)sinh(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + 3(\frac{\frac{-3}{2}(-2sinh(x)cosh(x) + 0)}{(-sinh^{2}(x) + 1)^{\frac{5}{2}}})sinh^{2}(x)cosh(x) + \frac{3*2sinh(x)cosh(x)cosh(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{3sinh^{2}(x)sinh(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + (\frac{\frac{-1}{2}(-2sinh(x)cosh(x) + 0)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}})cosh(x) + \frac{sinh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\\=&\frac{15sinh^{3}(x)cosh^{4}(x)}{(-sinh^{2}(x) + 1)^{\frac{7}{2}}} + \frac{9sinh(x)cosh^{4}(x)}{(-sinh^{2}(x) + 1)^{\frac{5}{2}}} + \frac{18sinh^{3}(x)cosh^{2}(x)}{(-sinh^{2}(x) + 1)^{\frac{5}{2}}} + \frac{10sinh(x)cosh^{2}(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{3sinh^{3}(x)}{(-sinh^{2}(x) + 1)^{\frac{3}{2}}} + \frac{sinh(x)}{(-sinh^{2}(x) + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

\[ \begin{equation}\begin{split}【2/4】求函数arccos(cosh(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arccos(cosh(x))\right)}{dx}\\=&(\frac{-(sinh(x))}{((1 - (cosh(x))^{2})^{\frac{1}{2}})})\\=&\frac{-sinh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-sinh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\right)}{dx}\\=&-(\frac{\frac{-1}{2}(-2cosh(x)sinh(x) + 0)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}})sinh(x) - \frac{cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\\=&\frac{-sinh^{2}(x)cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-sinh^{2}(x)cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\right)}{dx}\\=&-(\frac{\frac{-3}{2}(-2cosh(x)sinh(x) + 0)}{(-cosh^{2}(x) + 1)^{\frac{5}{2}}})sinh^{2}(x)cosh(x) - \frac{2sinh(x)cosh(x)cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sinh^{2}(x)sinh(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - (\frac{\frac{-1}{2}(-2cosh(x)sinh(x) + 0)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}})cosh(x) - \frac{sinh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\\=&\frac{-3sinh^{3}(x)cosh^{2}(x)}{(-cosh^{2}(x) + 1)^{\frac{5}{2}}} - \frac{3sinh(x)cosh^{2}(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sinh^{3}(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sinh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-3sinh^{3}(x)cosh^{2}(x)}{(-cosh^{2}(x) + 1)^{\frac{5}{2}}} - \frac{3sinh(x)cosh^{2}(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sinh^{3}(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{sinh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\right)}{dx}\\=&-3(\frac{\frac{-5}{2}(-2cosh(x)sinh(x) + 0)}{(-cosh^{2}(x) + 1)^{\frac{7}{2}}})sinh^{3}(x)cosh^{2}(x) - \frac{3*3sinh^{2}(x)cosh(x)cosh^{2}(x)}{(-cosh^{2}(x) + 1)^{\frac{5}{2}}} - \frac{3sinh^{3}(x)*2cosh(x)sinh(x)}{(-cosh^{2}(x) + 1)^{\frac{5}{2}}} - 3(\frac{\frac{-3}{2}(-2cosh(x)sinh(x) + 0)}{(-cosh^{2}(x) + 1)^{\frac{5}{2}}})sinh(x)cosh^{2}(x) - \frac{3cosh(x)cosh^{2}(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{3sinh(x)*2cosh(x)sinh(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - (\frac{\frac{-3}{2}(-2cosh(x)sinh(x) + 0)}{(-cosh^{2}(x) + 1)^{\frac{5}{2}}})sinh^{3}(x) - \frac{3sinh^{2}(x)cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - (\frac{\frac{-1}{2}(-2cosh(x)sinh(x) + 0)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}})sinh(x) - \frac{cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\\=&\frac{-15sinh^{4}(x)cosh^{3}(x)}{(-cosh^{2}(x) + 1)^{\frac{7}{2}}} - \frac{18sinh^{2}(x)cosh^{3}(x)}{(-cosh^{2}(x) + 1)^{\frac{5}{2}}} - \frac{9sinh^{4}(x)cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{5}{2}}} - \frac{3cosh^{3}(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{10sinh^{2}(x)cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{3}{2}}} - \frac{cosh(x)}{(-cosh^{2}(x) + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

\[ \begin{equation}\begin{split}【3/4】求函数arctan(tanh(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arctan(tanh(x))\right)}{dx}\\=&(\frac{(sech^{2}(x))}{(1 + (tanh(x))^{2})})\\=&\frac{sech^{2}(x)}{(tanh^{2}(x) + 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{sech^{2}(x)}{(tanh^{2}(x) + 1)}\right)}{dx}\\=&(\frac{-(2tanh(x)sech^{2}(x) + 0)}{(tanh^{2}(x) + 1)^{2}})sech^{2}(x) + \frac{-2sech(x)sech(x)tanh(x)}{(tanh^{2}(x) + 1)}\\=&\frac{-2tanh(x)sech^{4}(x)}{(tanh^{2}(x) + 1)^{2}} - \frac{2tanh(x)sech^{2}(x)}{(tanh^{2}(x) + 1)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2tanh(x)sech^{4}(x)}{(tanh^{2}(x) + 1)^{2}} - \frac{2tanh(x)sech^{2}(x)}{(tanh^{2}(x) + 1)}\right)}{dx}\\=&-2(\frac{-2(2tanh(x)sech^{2}(x) + 0)}{(tanh^{2}(x) + 1)^{3}})tanh(x)sech^{4}(x) - \frac{2sech^{2}(x)sech^{4}(x)}{(tanh^{2}(x) + 1)^{2}} - \frac{2tanh(x)*-4sech^{3}(x)sech(x)tanh(x)}{(tanh^{2}(x) + 1)^{2}} - 2(\frac{-(2tanh(x)sech^{2}(x) + 0)}{(tanh^{2}(x) + 1)^{2}})tanh(x)sech^{2}(x) - \frac{2sech^{2}(x)sech^{2}(x)}{(tanh^{2}(x) + 1)} - \frac{2tanh(x)*-2sech(x)sech(x)tanh(x)}{(tanh^{2}(x) + 1)}\\=&\frac{8tanh^{2}(x)sech^{6}(x)}{(tanh^{2}(x) + 1)^{3}} - \frac{2sech^{6}(x)}{(tanh^{2}(x) + 1)^{2}} + \frac{12tanh^{2}(x)sech^{4}(x)}{(tanh^{2}(x) + 1)^{2}} - \frac{2sech^{4}(x)}{(tanh^{2}(x) + 1)} + \frac{4tanh^{2}(x)sech^{2}(x)}{(tanh^{2}(x) + 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{8tanh^{2}(x)sech^{6}(x)}{(tanh^{2}(x) + 1)^{3}} - \frac{2sech^{6}(x)}{(tanh^{2}(x) + 1)^{2}} + \frac{12tanh^{2}(x)sech^{4}(x)}{(tanh^{2}(x) + 1)^{2}} - \frac{2sech^{4}(x)}{(tanh^{2}(x) + 1)} + \frac{4tanh^{2}(x)sech^{2}(x)}{(tanh^{2}(x) + 1)}\right)}{dx}\\=&8(\frac{-3(2tanh(x)sech^{2}(x) + 0)}{(tanh^{2}(x) + 1)^{4}})tanh^{2}(x)sech^{6}(x) + \frac{8*2tanh(x)sech^{2}(x)sech^{6}(x)}{(tanh^{2}(x) + 1)^{3}} + \frac{8tanh^{2}(x)*-6sech^{5}(x)sech(x)tanh(x)}{(tanh^{2}(x) + 1)^{3}} - 2(\frac{-2(2tanh(x)sech^{2}(x) + 0)}{(tanh^{2}(x) + 1)^{3}})sech^{6}(x) - \frac{2*-6sech^{5}(x)sech(x)tanh(x)}{(tanh^{2}(x) + 1)^{2}} + 12(\frac{-2(2tanh(x)sech^{2}(x) + 0)}{(tanh^{2}(x) + 1)^{3}})tanh^{2}(x)sech^{4}(x) + \frac{12*2tanh(x)sech^{2}(x)sech^{4}(x)}{(tanh^{2}(x) + 1)^{2}} + \frac{12tanh^{2}(x)*-4sech^{3}(x)sech(x)tanh(x)}{(tanh^{2}(x) + 1)^{2}} - 2(\frac{-(2tanh(x)sech^{2}(x) + 0)}{(tanh^{2}(x) + 1)^{2}})sech^{4}(x) - \frac{2*-4sech^{3}(x)sech(x)tanh(x)}{(tanh^{2}(x) + 1)} + 4(\frac{-(2tanh(x)sech^{2}(x) + 0)}{(tanh^{2}(x) + 1)^{2}})tanh^{2}(x)sech^{2}(x) + \frac{4*2tanh(x)sech^{2}(x)sech^{2}(x)}{(tanh^{2}(x) + 1)} + \frac{4tanh^{2}(x)*-2sech(x)sech(x)tanh(x)}{(tanh^{2}(x) + 1)}\\=&\frac{-48tanh^{3}(x)sech^{8}(x)}{(tanh^{2}(x) + 1)^{4}} + \frac{24tanh(x)sech^{8}(x)}{(tanh^{2}(x) + 1)^{3}} - \frac{96tanh^{3}(x)sech^{6}(x)}{(tanh^{2}(x) + 1)^{3}} + \frac{40tanh(x)sech^{6}(x)}{(tanh^{2}(x) + 1)^{2}} - \frac{56tanh^{3}(x)sech^{4}(x)}{(tanh^{2}(x) + 1)^{2}} + \frac{16tanh(x)sech^{4}(x)}{(tanh^{2}(x) + 1)} - \frac{8tanh^{3}(x)sech^{2}(x)}{(tanh^{2}(x) + 1)}\\ \end{split}\end{equation} \]

\[ \begin{equation}\begin{split}【4/4】求函数arccot(coth(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arccot(coth(x))\right)}{dx}\\=&(\frac{(-csch^{2}(x))}{(1 + (coth(x))^{2})})\\=&\frac{-csch^{2}(x)}{(coth^{2}(x) + 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-csch^{2}(x)}{(coth^{2}(x) + 1)}\right)}{dx}\\=&-(\frac{-(-2coth(x)csch^{2}(x) + 0)}{(coth^{2}(x) + 1)^{2}})csch^{2}(x) + \frac{--2csch(x)csch(x)coth(x)}{(coth^{2}(x) + 1)}\\=&\frac{-2coth(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{2coth(x)csch^{2}(x)}{(coth^{2}(x) + 1)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-2coth(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{2coth(x)csch^{2}(x)}{(coth^{2}(x) + 1)}\right)}{dx}\\=&-2(\frac{-2(-2coth(x)csch^{2}(x) + 0)}{(coth^{2}(x) + 1)^{3}})coth(x)csch^{4}(x) + \frac{-2*-csch^{2}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{-2coth(x)*-4csch^{3}(x)csch(x)coth(x)}{(coth^{2}(x) + 1)^{2}} + 2(\frac{-(-2coth(x)csch^{2}(x) + 0)}{(coth^{2}(x) + 1)^{2}})coth(x)csch^{2}(x) + \frac{2*-csch^{2}(x)csch^{2}(x)}{(coth^{2}(x) + 1)} + \frac{2coth(x)*-2csch(x)csch(x)coth(x)}{(coth^{2}(x) + 1)}\\=&\frac{-8coth^{2}(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{3}} + \frac{2csch^{6}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{8coth^{2}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{4coth^{2}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{-2csch^{4}(x)}{(coth^{2}(x) + 1)} + \frac{-4coth^{2}(x)csch^{2}(x)}{(coth^{2}(x) + 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-8coth^{2}(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{3}} + \frac{2csch^{6}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{8coth^{2}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{4coth^{2}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{-2csch^{4}(x)}{(coth^{2}(x) + 1)} + \frac{-4coth^{2}(x)csch^{2}(x)}{(coth^{2}(x) + 1)}\right)}{dx}\\=&-8(\frac{-3(-2coth(x)csch^{2}(x) + 0)}{(coth^{2}(x) + 1)^{4}})coth^{2}(x)csch^{6}(x) + \frac{-8*-2coth(x)csch^{2}(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{3}} + \frac{-8coth^{2}(x)*-6csch^{5}(x)csch(x)coth(x)}{(coth^{2}(x) + 1)^{3}} + 2(\frac{-2(-2coth(x)csch^{2}(x) + 0)}{(coth^{2}(x) + 1)^{3}})csch^{6}(x) + \frac{2*-6csch^{5}(x)csch(x)coth(x)}{(coth^{2}(x) + 1)^{2}} + 8(\frac{-2(-2coth(x)csch^{2}(x) + 0)}{(coth^{2}(x) + 1)^{3}})coth^{2}(x)csch^{4}(x) + \frac{8*-2coth(x)csch^{2}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{8coth^{2}(x)*-4csch^{3}(x)csch(x)coth(x)}{(coth^{2}(x) + 1)^{2}} + 4(\frac{-2(-2coth(x)csch^{2}(x) + 0)}{(coth^{2}(x) + 1)^{3}})coth^{2}(x)csch^{4}(x) + \frac{4*-2coth(x)csch^{2}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{4coth^{2}(x)*-4csch^{3}(x)csch(x)coth(x)}{(coth^{2}(x) + 1)^{2}} + -2(\frac{-(-2coth(x)csch^{2}(x) + 0)}{(coth^{2}(x) + 1)^{2}})csch^{4}(x) + \frac{-2*-4csch^{3}(x)csch(x)coth(x)}{(coth^{2}(x) + 1)} + -4(\frac{-(-2coth(x)csch^{2}(x) + 0)}{(coth^{2}(x) + 1)^{2}})coth^{2}(x)csch^{2}(x) + \frac{-4*-2coth(x)csch^{2}(x)csch^{2}(x)}{(coth^{2}(x) + 1)} + \frac{-4coth^{2}(x)*-2csch(x)csch(x)coth(x)}{(coth^{2}(x) + 1)}\\=&\frac{-48coth^{3}(x)csch^{8}(x)}{(coth^{2}(x) + 1)^{4}} + \frac{16coth(x)csch^{8}(x)}{(coth^{2}(x) + 1)^{3}} + \frac{48coth^{3}(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{3}} + \frac{8coth(x)csch^{8}(x)}{(coth^{2}(x) + 1)^{3}} + \frac{-12coth(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{32coth^{3}(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{3}} + \frac{-16coth(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{-32coth^{3}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{16coth^{3}(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{3}} + \frac{-8coth(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{-16coth^{3}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{-4coth(x)csch^{6}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{16coth(x)csch^{4}(x)}{(coth^{2}(x) + 1)} + \frac{-8coth^{3}(x)csch^{4}(x)}{(coth^{2}(x) + 1)^{2}} + \frac{8coth^{3}(x)csch^{2}(x)}{(coth^{2}(x) + 1)}\\ \end{split}\end{equation} \]

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