Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{tanh(x)}^{th(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{tanh(x)}^{th(x)}\right)}{dx}\\=&(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})\\=&\frac{-th(x)}{ln(tanh(x))} + \frac{1}{ln(tanh(x))th(x)} - \frac{log_{tanh(x)}^{th(x)}sech^{2}(x)}{ln(tanh(x))tanh(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-th(x)}{ln(tanh(x))} + \frac{1}{ln(tanh(x))th(x)} - \frac{log_{tanh(x)}^{th(x)}sech^{2}(x)}{ln(tanh(x))tanh(x)}\right)}{dx}\\=&\frac{--sech^{2}(x)th(x)}{ln^{2}(tanh(x))(tanh(x))} - \frac{(1 - th^{2}(x))}{ln(tanh(x))} + \frac{-sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))th(x)} + \frac{-(1 - th^{2}(x))}{ln(tanh(x))th^{2}(x)} - \frac{(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{2}(x)}{ln(tanh(x))tanh(x)} - \frac{log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))tanh(x)} - \frac{log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{2}(x)}{ln(tanh(x))tanh^{2}(x)} - \frac{log_{tanh(x)}^{th(x)}*-2sech(x)sech(x)tanh(x)}{ln(tanh(x))tanh(x)}\\=&\frac{2th(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2sech^{2}(x)}{ln^{2}(tanh(x))th(x)tanh(x)} - \frac{1}{ln(tanh(x))th^{2}(x)} + \frac{th^{2}(x)}{ln(tanh(x))} + \frac{2log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{2log_{tanh(x)}^{th(x)}sech^{2}(x)}{ln(tanh(x))}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2th(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2sech^{2}(x)}{ln^{2}(tanh(x))th(x)tanh(x)} - \frac{1}{ln(tanh(x))th^{2}(x)} + \frac{th^{2}(x)}{ln(tanh(x))} + \frac{2log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{2log_{tanh(x)}^{th(x)}sech^{2}(x)}{ln(tanh(x))}\right)}{dx}\\=&\frac{2*-2sech^{2}(x)th(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))tanh(x)} + \frac{2(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{2th(x)*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{2th(x)*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2*-2sech^{2}(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))th(x)tanh(x)} - \frac{2*-(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh(x)} - \frac{2*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))th(x)tanh^{2}(x)} - \frac{2*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))th(x)tanh(x)} - \frac{-sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))th^{2}(x)} - \frac{-2(1 - th^{2}(x))}{ln(tanh(x))th^{3}(x)} + \frac{-sech^{2}(x)th^{2}(x)}{ln^{2}(tanh(x))(tanh(x))} + \frac{2th(x)(1 - th^{2}(x))}{ln(tanh(x))} + \frac{2(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{2log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))(tanh(x))tanh^{2}(x)} + \frac{2log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} + \frac{2log_{tanh(x)}^{th(x)}*-4sech^{3}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{4}(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))(tanh(x))tanh^{2}(x)} + \frac{log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{4}(x)}{ln(tanh(x))tanh^{3}(x)} + \frac{log_{tanh(x)}^{th(x)}*-4sech^{3}(x)sech(x)tanh(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{2(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{2}(x)}{ln(tanh(x))} + \frac{2log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))} + \frac{2log_{tanh(x)}^{th(x)}*-2sech(x)sech(x)tanh(x)}{ln(tanh(x))}\\=&\frac{-6th(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{3th(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{3sech^{4}(x)}{ln^{2}(tanh(x))th(x)tanh^{2}(x)} - \frac{6th(x)sech^{2}(x)}{ln^{2}(tanh(x))} + \frac{6sech^{4}(x)}{ln^{3}(tanh(x))th(x)tanh^{2}(x)} + \frac{3sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh(x)} - \frac{3th^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{6sech^{2}(x)}{ln^{2}(tanh(x))th(x)} + \frac{2}{ln(tanh(x))th^{3}(x)} - \frac{2}{ln(tanh(x))th(x)} + \frac{2th(x)}{ln(tanh(x))} - \frac{2th^{3}(x)}{ln(tanh(x))} - \frac{6log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{12log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln(tanh(x))tanh^{3}(x)} - \frac{4log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))tanh(x)} - \frac{4log_{tanh(x)}^{th(x)}tanh(x)sech^{2}(x)}{ln(tanh(x))}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6th(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{3th(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{3sech^{4}(x)}{ln^{2}(tanh(x))th(x)tanh^{2}(x)} - \frac{6th(x)sech^{2}(x)}{ln^{2}(tanh(x))} + \frac{6sech^{4}(x)}{ln^{3}(tanh(x))th(x)tanh^{2}(x)} + \frac{3sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh(x)} - \frac{3th^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{6sech^{2}(x)}{ln^{2}(tanh(x))th(x)} + \frac{2}{ln(tanh(x))th^{3}(x)} - \frac{2}{ln(tanh(x))th(x)} + \frac{2th(x)}{ln(tanh(x))} - \frac{2th^{3}(x)}{ln(tanh(x))} - \frac{6log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{12log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln(tanh(x))tanh^{3}(x)} - \frac{4log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))tanh(x)} - \frac{4log_{tanh(x)}^{th(x)}tanh(x)sech^{2}(x)}{ln(tanh(x))}\right)}{dx}\\=&\frac{-6*-3sech^{2}(x)th(x)sech^{4}(x)}{ln^{4}(tanh(x))(tanh(x))tanh^{2}(x)} - \frac{6(1 - th^{2}(x))sech^{4}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{6th(x)*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6th(x)*-4sech^{3}(x)sech(x)tanh(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{3*-2sech^{2}(x)th(x)sech^{4}(x)}{ln^{3}(tanh(x))(tanh(x))tanh^{2}(x)} - \frac{3(1 - th^{2}(x))sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} - \frac{3th(x)*-2sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{3th(x)*-4sech^{3}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{3*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))(tanh(x))th(x)tanh^{2}(x)} + \frac{3*-(1 - th^{2}(x))sech^{4}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh^{2}(x)} + \frac{3*-2sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))th(x)tanh^{3}(x)} + \frac{3*-4sech^{3}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))th(x)tanh^{2}(x)} - \frac{6*-2sech^{2}(x)th(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))} - \frac{6(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))} - \frac{6th(x)*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))} + \frac{6*-3sech^{2}(x)sech^{4}(x)}{ln^{4}(tanh(x))(tanh(x))th(x)tanh^{2}(x)} + \frac{6*-(1 - th^{2}(x))sech^{4}(x)}{ln^{3}(tanh(x))th^{2}(x)tanh^{2}(x)} + \frac{6*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))th(x)tanh^{3}(x)} + \frac{6*-4sech^{3}(x)sech(x)tanh(x)}{ln^{3}(tanh(x))th(x)tanh^{2}(x)} + \frac{3*-2sech^{2}(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))th^{2}(x)tanh(x)} + \frac{3*-2(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))th^{3}(x)tanh(x)} + \frac{3*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh^{2}(x)} + \frac{3*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))th^{2}(x)tanh(x)} - \frac{3*-2sech^{2}(x)th^{2}(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))tanh(x)} - \frac{3*2th(x)(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{3th^{2}(x)*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} - \frac{3th^{2}(x)*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{6*-2sech^{2}(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))th(x)} + \frac{6*-(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)} + \frac{6*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))th(x)} + \frac{2*-sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))th^{3}(x)} + \frac{2*-3(1 - th^{2}(x))}{ln(tanh(x))th^{4}(x)} - \frac{2*-sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))th(x)} - \frac{2*-(1 - th^{2}(x))}{ln(tanh(x))th^{2}(x)} + \frac{2*-sech^{2}(x)th(x)}{ln^{2}(tanh(x))(tanh(x))} + \frac{2(1 - th^{2}(x))}{ln(tanh(x))} - \frac{2*-sech^{2}(x)th^{3}(x)}{ln^{2}(tanh(x))(tanh(x))} - \frac{2*3th^{2}(x)(1 - th^{2}(x))}{ln(tanh(x))} - \frac{6(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{6}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-3sech^{2}(x)sech^{6}(x)}{ln^{4}(tanh(x))(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-3sech^{2}(x)sech^{6}(x)}{ln^{3}(tanh(x))tanh^{4}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-6sech^{5}(x)sech(x)tanh(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{6}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{6}(x)}{ln^{3}(tanh(x))(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-3sech^{2}(x)sech^{6}(x)}{ln^{2}(tanh(x))tanh^{4}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-6sech^{5}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{12(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{4}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{12log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))(tanh(x))tanh(x)} - \frac{12log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} - \frac{12log_{tanh(x)}^{th(x)}*-4sech^{3}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{6}(x)}{ln(tanh(x))tanh^{3}(x)} - \frac{2log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{6}(x)}{ln^{2}(tanh(x))(tanh(x))tanh^{3}(x)} - \frac{2log_{tanh(x)}^{th(x)}*-3sech^{2}(x)sech^{6}(x)}{ln(tanh(x))tanh^{4}(x)} - \frac{2log_{tanh(x)}^{th(x)}*-6sech^{5}(x)sech(x)tanh(x)}{ln(tanh(x))tanh^{3}(x)} - \frac{4(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{4}(x)}{ln(tanh(x))tanh(x)} - \frac{4log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))(tanh(x))tanh(x)} - \frac{4log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{4}(x)}{ln(tanh(x))tanh^{2}(x)} - \frac{4log_{tanh(x)}^{th(x)}*-4sech^{3}(x)sech(x)tanh(x)}{ln(tanh(x))tanh(x)} - \frac{4(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})tanh(x)sech^{2}(x)}{ln(tanh(x))} - \frac{4log_{tanh(x)}^{th(x)}*-sech^{2}(x)tanh(x)sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))} - \frac{4log_{tanh(x)}^{th(x)}sech^{2}(x)sech^{2}(x)}{ln(tanh(x))} - \frac{4log_{tanh(x)}^{th(x)}tanh(x)*-2sech(x)sech(x)tanh(x)}{ln(tanh(x))}\\=&\frac{24th(x)sech^{6}(x)}{ln^{4}(tanh(x))tanh^{3}(x)} + \frac{24th(x)sech^{6}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} + \frac{8th(x)sech^{6}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} + \frac{48th(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh(x)} - \frac{8sech^{6}(x)}{ln^{2}(tanh(x))th(x)tanh^{3}(x)} + \frac{16th(x)tanh(x)sech^{2}(x)}{ln^{2}(tanh(x))} + \frac{16th(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{24sech^{6}(x)}{ln^{3}(tanh(x))th(x)tanh^{3}(x)} - \frac{6sech^{4}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh^{2}(x)} - \frac{16sech^{4}(x)}{ln^{2}(tanh(x))th(x)tanh(x)} + \frac{12th^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))} - \frac{24sech^{6}(x)}{ln^{4}(tanh(x))th(x)tanh^{3}(x)} - \frac{12sech^{4}(x)}{ln^{3}(tanh(x))th^{2}(x)tanh^{2}(x)} + \frac{6th^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} - \frac{48sech^{4}(x)}{ln^{3}(tanh(x))th(x)tanh(x)} - \frac{8sech^{2}(x)}{ln^{2}(tanh(x))th^{3}(x)tanh(x)} + \frac{8sech^{2}(x)}{ln^{2}(tanh(x))th(x)tanh(x)} - \frac{16tanh(x)sech^{2}(x)}{ln^{2}(tanh(x))th(x)} - \frac{12sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)} + \frac{12th^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{8th(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{8th^{3}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{6}{ln(tanh(x))th^{4}(x)} + \frac{8}{ln(tanh(x))th^{2}(x)} - \frac{8th^{2}(x)}{ln(tanh(x))} + \frac{6th^{4}(x)}{ln(tanh(x))} + \frac{24log_{tanh(x)}^{th(x)}sech^{8}(x)}{ln^{4}(tanh(x))tanh^{4}(x)} + \frac{36log_{tanh(x)}^{th(x)}sech^{8}(x)}{ln^{3}(tanh(x))tanh^{4}(x)} + \frac{72log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} + \frac{22log_{tanh(x)}^{th(x)}sech^{8}(x)}{ln^{2}(tanh(x))tanh^{4}(x)} + \frac{56log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{56log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))} + \frac{6log_{tanh(x)}^{th(x)}sech^{8}(x)}{ln(tanh(x))tanh^{4}(x)} + \frac{16log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{12log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))} + \frac{8log_{tanh(x)}^{th(x)}tanh^{2}(x)sech^{2}(x)}{ln(tanh(x))}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{tanh(x)}^{th(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{tanh(x)}^{th(x)}\right)}{dx}\\=&(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})\\=&\frac{-th(x)}{ln(tanh(x))} + \frac{1}{ln(tanh(x))th(x)} - \frac{log_{tanh(x)}^{th(x)}sech^{2}(x)}{ln(tanh(x))tanh(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-th(x)}{ln(tanh(x))} + \frac{1}{ln(tanh(x))th(x)} - \frac{log_{tanh(x)}^{th(x)}sech^{2}(x)}{ln(tanh(x))tanh(x)}\right)}{dx}\\=&\frac{--sech^{2}(x)th(x)}{ln^{2}(tanh(x))(tanh(x))} - \frac{(1 - th^{2}(x))}{ln(tanh(x))} + \frac{-sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))th(x)} + \frac{-(1 - th^{2}(x))}{ln(tanh(x))th^{2}(x)} - \frac{(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{2}(x)}{ln(tanh(x))tanh(x)} - \frac{log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))tanh(x)} - \frac{log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{2}(x)}{ln(tanh(x))tanh^{2}(x)} - \frac{log_{tanh(x)}^{th(x)}*-2sech(x)sech(x)tanh(x)}{ln(tanh(x))tanh(x)}\\=&\frac{2th(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2sech^{2}(x)}{ln^{2}(tanh(x))th(x)tanh(x)} - \frac{1}{ln(tanh(x))th^{2}(x)} + \frac{th^{2}(x)}{ln(tanh(x))} + \frac{2log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{2log_{tanh(x)}^{th(x)}sech^{2}(x)}{ln(tanh(x))}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2th(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2sech^{2}(x)}{ln^{2}(tanh(x))th(x)tanh(x)} - \frac{1}{ln(tanh(x))th^{2}(x)} + \frac{th^{2}(x)}{ln(tanh(x))} + \frac{2log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{2log_{tanh(x)}^{th(x)}sech^{2}(x)}{ln(tanh(x))}\right)}{dx}\\=&\frac{2*-2sech^{2}(x)th(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))tanh(x)} + \frac{2(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{2th(x)*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{2th(x)*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2*-2sech^{2}(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))th(x)tanh(x)} - \frac{2*-(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh(x)} - \frac{2*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))th(x)tanh^{2}(x)} - \frac{2*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))th(x)tanh(x)} - \frac{-sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))th^{2}(x)} - \frac{-2(1 - th^{2}(x))}{ln(tanh(x))th^{3}(x)} + \frac{-sech^{2}(x)th^{2}(x)}{ln^{2}(tanh(x))(tanh(x))} + \frac{2th(x)(1 - th^{2}(x))}{ln(tanh(x))} + \frac{2(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{2log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))(tanh(x))tanh^{2}(x)} + \frac{2log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} + \frac{2log_{tanh(x)}^{th(x)}*-4sech^{3}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{4}(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))(tanh(x))tanh^{2}(x)} + \frac{log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{4}(x)}{ln(tanh(x))tanh^{3}(x)} + \frac{log_{tanh(x)}^{th(x)}*-4sech^{3}(x)sech(x)tanh(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{2(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{2}(x)}{ln(tanh(x))} + \frac{2log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))} + \frac{2log_{tanh(x)}^{th(x)}*-2sech(x)sech(x)tanh(x)}{ln(tanh(x))}\\=&\frac{-6th(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{3th(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{3sech^{4}(x)}{ln^{2}(tanh(x))th(x)tanh^{2}(x)} - \frac{6th(x)sech^{2}(x)}{ln^{2}(tanh(x))} + \frac{6sech^{4}(x)}{ln^{3}(tanh(x))th(x)tanh^{2}(x)} + \frac{3sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh(x)} - \frac{3th^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{6sech^{2}(x)}{ln^{2}(tanh(x))th(x)} + \frac{2}{ln(tanh(x))th^{3}(x)} - \frac{2}{ln(tanh(x))th(x)} + \frac{2th(x)}{ln(tanh(x))} - \frac{2th^{3}(x)}{ln(tanh(x))} - \frac{6log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{12log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln(tanh(x))tanh^{3}(x)} - \frac{4log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))tanh(x)} - \frac{4log_{tanh(x)}^{th(x)}tanh(x)sech^{2}(x)}{ln(tanh(x))}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6th(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{3th(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{3sech^{4}(x)}{ln^{2}(tanh(x))th(x)tanh^{2}(x)} - \frac{6th(x)sech^{2}(x)}{ln^{2}(tanh(x))} + \frac{6sech^{4}(x)}{ln^{3}(tanh(x))th(x)tanh^{2}(x)} + \frac{3sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh(x)} - \frac{3th^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{6sech^{2}(x)}{ln^{2}(tanh(x))th(x)} + \frac{2}{ln(tanh(x))th^{3}(x)} - \frac{2}{ln(tanh(x))th(x)} + \frac{2th(x)}{ln(tanh(x))} - \frac{2th^{3}(x)}{ln(tanh(x))} - \frac{6log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{12log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln(tanh(x))tanh^{3}(x)} - \frac{4log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))tanh(x)} - \frac{4log_{tanh(x)}^{th(x)}tanh(x)sech^{2}(x)}{ln(tanh(x))}\right)}{dx}\\=&\frac{-6*-3sech^{2}(x)th(x)sech^{4}(x)}{ln^{4}(tanh(x))(tanh(x))tanh^{2}(x)} - \frac{6(1 - th^{2}(x))sech^{4}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{6th(x)*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6th(x)*-4sech^{3}(x)sech(x)tanh(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{3*-2sech^{2}(x)th(x)sech^{4}(x)}{ln^{3}(tanh(x))(tanh(x))tanh^{2}(x)} - \frac{3(1 - th^{2}(x))sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} - \frac{3th(x)*-2sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{3th(x)*-4sech^{3}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{3*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))(tanh(x))th(x)tanh^{2}(x)} + \frac{3*-(1 - th^{2}(x))sech^{4}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh^{2}(x)} + \frac{3*-2sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))th(x)tanh^{3}(x)} + \frac{3*-4sech^{3}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))th(x)tanh^{2}(x)} - \frac{6*-2sech^{2}(x)th(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))} - \frac{6(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))} - \frac{6th(x)*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))} + \frac{6*-3sech^{2}(x)sech^{4}(x)}{ln^{4}(tanh(x))(tanh(x))th(x)tanh^{2}(x)} + \frac{6*-(1 - th^{2}(x))sech^{4}(x)}{ln^{3}(tanh(x))th^{2}(x)tanh^{2}(x)} + \frac{6*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))th(x)tanh^{3}(x)} + \frac{6*-4sech^{3}(x)sech(x)tanh(x)}{ln^{3}(tanh(x))th(x)tanh^{2}(x)} + \frac{3*-2sech^{2}(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))th^{2}(x)tanh(x)} + \frac{3*-2(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))th^{3}(x)tanh(x)} + \frac{3*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh^{2}(x)} + \frac{3*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))th^{2}(x)tanh(x)} - \frac{3*-2sech^{2}(x)th^{2}(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))tanh(x)} - \frac{3*2th(x)(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{3th^{2}(x)*-sech^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} - \frac{3th^{2}(x)*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{6*-2sech^{2}(x)sech^{2}(x)}{ln^{3}(tanh(x))(tanh(x))th(x)} + \frac{6*-(1 - th^{2}(x))sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)} + \frac{6*-2sech(x)sech(x)tanh(x)}{ln^{2}(tanh(x))th(x)} + \frac{2*-sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))th^{3}(x)} + \frac{2*-3(1 - th^{2}(x))}{ln(tanh(x))th^{4}(x)} - \frac{2*-sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))th(x)} - \frac{2*-(1 - th^{2}(x))}{ln(tanh(x))th^{2}(x)} + \frac{2*-sech^{2}(x)th(x)}{ln^{2}(tanh(x))(tanh(x))} + \frac{2(1 - th^{2}(x))}{ln(tanh(x))} - \frac{2*-sech^{2}(x)th^{3}(x)}{ln^{2}(tanh(x))(tanh(x))} - \frac{2*3th^{2}(x)(1 - th^{2}(x))}{ln(tanh(x))} - \frac{6(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{6}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-3sech^{2}(x)sech^{6}(x)}{ln^{4}(tanh(x))(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-3sech^{2}(x)sech^{6}(x)}{ln^{3}(tanh(x))tanh^{4}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-6sech^{5}(x)sech(x)tanh(x)}{ln^{3}(tanh(x))tanh^{3}(x)} - \frac{6(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{6}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{6}(x)}{ln^{3}(tanh(x))(tanh(x))tanh^{3}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-3sech^{2}(x)sech^{6}(x)}{ln^{2}(tanh(x))tanh^{4}(x)} - \frac{6log_{tanh(x)}^{th(x)}*-6sech^{5}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh^{3}(x)} - \frac{12(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{4}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{12log_{tanh(x)}^{th(x)}*-2sech^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))(tanh(x))tanh(x)} - \frac{12log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} - \frac{12log_{tanh(x)}^{th(x)}*-4sech^{3}(x)sech(x)tanh(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{2(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{6}(x)}{ln(tanh(x))tanh^{3}(x)} - \frac{2log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{6}(x)}{ln^{2}(tanh(x))(tanh(x))tanh^{3}(x)} - \frac{2log_{tanh(x)}^{th(x)}*-3sech^{2}(x)sech^{6}(x)}{ln(tanh(x))tanh^{4}(x)} - \frac{2log_{tanh(x)}^{th(x)}*-6sech^{5}(x)sech(x)tanh(x)}{ln(tanh(x))tanh^{3}(x)} - \frac{4(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})sech^{4}(x)}{ln(tanh(x))tanh(x)} - \frac{4log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))(tanh(x))tanh(x)} - \frac{4log_{tanh(x)}^{th(x)}*-sech^{2}(x)sech^{4}(x)}{ln(tanh(x))tanh^{2}(x)} - \frac{4log_{tanh(x)}^{th(x)}*-4sech^{3}(x)sech(x)tanh(x)}{ln(tanh(x))tanh(x)} - \frac{4(\frac{(\frac{((1 - th^{2}(x)))}{(th(x))} - \frac{(sech^{2}(x))log_{tanh(x)}^{th(x)}}{(tanh(x))})}{(ln(tanh(x)))})tanh(x)sech^{2}(x)}{ln(tanh(x))} - \frac{4log_{tanh(x)}^{th(x)}*-sech^{2}(x)tanh(x)sech^{2}(x)}{ln^{2}(tanh(x))(tanh(x))} - \frac{4log_{tanh(x)}^{th(x)}sech^{2}(x)sech^{2}(x)}{ln(tanh(x))} - \frac{4log_{tanh(x)}^{th(x)}tanh(x)*-2sech(x)sech(x)tanh(x)}{ln(tanh(x))}\\=&\frac{24th(x)sech^{6}(x)}{ln^{4}(tanh(x))tanh^{3}(x)} + \frac{24th(x)sech^{6}(x)}{ln^{3}(tanh(x))tanh^{3}(x)} + \frac{8th(x)sech^{6}(x)}{ln^{2}(tanh(x))tanh^{3}(x)} + \frac{48th(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh(x)} - \frac{8sech^{6}(x)}{ln^{2}(tanh(x))th(x)tanh^{3}(x)} + \frac{16th(x)tanh(x)sech^{2}(x)}{ln^{2}(tanh(x))} + \frac{16th(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{24sech^{6}(x)}{ln^{3}(tanh(x))th(x)tanh^{3}(x)} - \frac{6sech^{4}(x)}{ln^{2}(tanh(x))th^{2}(x)tanh^{2}(x)} - \frac{16sech^{4}(x)}{ln^{2}(tanh(x))th(x)tanh(x)} + \frac{12th^{2}(x)sech^{2}(x)}{ln^{2}(tanh(x))} - \frac{24sech^{6}(x)}{ln^{4}(tanh(x))th(x)tanh^{3}(x)} - \frac{12sech^{4}(x)}{ln^{3}(tanh(x))th^{2}(x)tanh^{2}(x)} + \frac{6th^{2}(x)sech^{4}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} - \frac{48sech^{4}(x)}{ln^{3}(tanh(x))th(x)tanh(x)} - \frac{8sech^{2}(x)}{ln^{2}(tanh(x))th^{3}(x)tanh(x)} + \frac{8sech^{2}(x)}{ln^{2}(tanh(x))th(x)tanh(x)} - \frac{16tanh(x)sech^{2}(x)}{ln^{2}(tanh(x))th(x)} - \frac{12sech^{2}(x)}{ln^{2}(tanh(x))th^{2}(x)} + \frac{12th^{2}(x)sech^{4}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} - \frac{8th(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} + \frac{8th^{3}(x)sech^{2}(x)}{ln^{2}(tanh(x))tanh(x)} - \frac{6}{ln(tanh(x))th^{4}(x)} + \frac{8}{ln(tanh(x))th^{2}(x)} - \frac{8th^{2}(x)}{ln(tanh(x))} + \frac{6th^{4}(x)}{ln(tanh(x))} + \frac{24log_{tanh(x)}^{th(x)}sech^{8}(x)}{ln^{4}(tanh(x))tanh^{4}(x)} + \frac{36log_{tanh(x)}^{th(x)}sech^{8}(x)}{ln^{3}(tanh(x))tanh^{4}(x)} + \frac{72log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{3}(tanh(x))tanh^{2}(x)} + \frac{22log_{tanh(x)}^{th(x)}sech^{8}(x)}{ln^{2}(tanh(x))tanh^{4}(x)} + \frac{56log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln^{2}(tanh(x))tanh^{2}(x)} + \frac{56log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln^{2}(tanh(x))} + \frac{6log_{tanh(x)}^{th(x)}sech^{8}(x)}{ln(tanh(x))tanh^{4}(x)} + \frac{16log_{tanh(x)}^{th(x)}sech^{6}(x)}{ln(tanh(x))tanh^{2}(x)} + \frac{12log_{tanh(x)}^{th(x)}sech^{4}(x)}{ln(tanh(x))} + \frac{8log_{tanh(x)}^{th(x)}tanh^{2}(x)sech^{2}(x)}{ln(tanh(x))}\\ \end{split}\end{equation} \]