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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{-xlg(tan(e^{x}))}{2} + \frac{xlg(th(e^{x}))}{4} + {\frac{1}{2}}^{e^{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-1}{2}xlg(tan(e^{x})) + \frac{1}{4}xlg(th(e^{x})) + {\frac{1}{2}}^{e^{x}}\right)}{dx}\\=&\frac{-1}{2}lg(tan(e^{x})) - \frac{\frac{1}{2}xsec^{2}(e^{x})(e^{x})}{ln{10}(tan(e^{x}))} + \frac{1}{4}lg(th(e^{x})) + \frac{\frac{1}{4}x(1 - th^{2}(e^{x}))e^{x}}{ln{10}(th(e^{x}))} + ({\frac{1}{2}}^{e^{x}}((e^{x})ln(\frac{1}{2}) + \frac{(e^{x})(0)}{(\frac{1}{2})}))\\=&\frac{-lg(tan(e^{x}))}{2} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} + \frac{lg(th(e^{x}))}{4} + \frac{xe^{x}}{4ln{10}th(e^{x})} - \frac{xe^{x}th(e^{x})}{4ln{10}} + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2})\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-lg(tan(e^{x}))}{2} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} + \frac{lg(th(e^{x}))}{4} + \frac{xe^{x}}{4ln{10}th(e^{x})} - \frac{xe^{x}th(e^{x})}{4ln{10}} + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2})\right)}{dx}\\=&\frac{-sec^{2}(e^{x})(e^{x})}{2ln{10}(tan(e^{x}))} - \frac{e^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} - \frac{xe^{x}*-0sec^{2}(e^{x})}{2ln^{2}{10}tan(e^{x})} - \frac{xe^{x}*-sec^{2}(e^{x})(e^{x})sec^{2}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{xe^{x}*2sec^{2}(e^{x})tan(e^{x})e^{x}}{2ln{10}tan(e^{x})} + \frac{(1 - th^{2}(e^{x}))e^{x}}{4ln{10}(th(e^{x}))} + \frac{e^{x}}{4ln{10}th(e^{x})} + \frac{xe^{x}}{4ln{10}th(e^{x})} + \frac{xe^{x}*-0}{4ln^{2}{10}th(e^{x})} + \frac{xe^{x}*-(1 - th^{2}(e^{x}))e^{x}}{4ln{10}th^{2}(e^{x})} - \frac{e^{x}th(e^{x})}{4ln{10}} - \frac{xe^{x}th(e^{x})}{4ln{10}} - \frac{xe^{x}*-0th(e^{x})}{4ln^{2}{10}} - \frac{xe^{x}(1 - th^{2}(e^{x}))e^{x}}{4ln{10}} + ({\frac{1}{2}}^{e^{x}}((e^{x})ln(\frac{1}{2}) + \frac{(e^{x})(0)}{(\frac{1}{2})}))e^{x}ln(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2}) + \frac{{\frac{1}{2}}^{e^{x}}e^{x}*0}{(\frac{1}{2})}\\=&\frac{-e^{x}sec^{2}(e^{x})}{ln{10}tan(e^{x})} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} + \frac{xe^{{x}*{2}}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{xe^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} + \frac{e^{x}}{2ln{10}th(e^{x})} - \frac{e^{x}th(e^{x})}{2ln{10}} + \frac{xe^{x}}{4ln{10}th(e^{x})} - \frac{xe^{{x}*{2}}}{4ln{10}th^{2}(e^{x})} - \frac{xe^{x}th(e^{x})}{4ln{10}} + \frac{xe^{{x}*{2}}th^{2}(e^{x})}{4ln{10}} + {\frac{1}{2}}^{e^{x}}e^{{x}*{2}}ln^{2}(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2})\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-e^{x}sec^{2}(e^{x})}{ln{10}tan(e^{x})} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} + \frac{xe^{{x}*{2}}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{xe^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} + \frac{e^{x}}{2ln{10}th(e^{x})} - \frac{e^{x}th(e^{x})}{2ln{10}} + \frac{xe^{x}}{4ln{10}th(e^{x})} - \frac{xe^{{x}*{2}}}{4ln{10}th^{2}(e^{x})} - \frac{xe^{x}th(e^{x})}{4ln{10}} + \frac{xe^{{x}*{2}}th^{2}(e^{x})}{4ln{10}} + {\frac{1}{2}}^{e^{x}}e^{{x}*{2}}ln^{2}(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2})\right)}{dx}\\=&\frac{-e^{x}sec^{2}(e^{x})}{ln{10}tan(e^{x})} - \frac{e^{x}*-0sec^{2}(e^{x})}{ln^{2}{10}tan(e^{x})} - \frac{e^{x}*-sec^{2}(e^{x})(e^{x})sec^{2}(e^{x})}{ln{10}tan^{2}(e^{x})} - \frac{e^{x}*2sec^{2}(e^{x})tan(e^{x})e^{x}}{ln{10}tan(e^{x})} - \frac{e^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} - \frac{xe^{x}*-0sec^{2}(e^{x})}{2ln^{2}{10}tan(e^{x})} - \frac{xe^{x}*-sec^{2}(e^{x})(e^{x})sec^{2}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{xe^{x}*2sec^{2}(e^{x})tan(e^{x})e^{x}}{2ln{10}tan(e^{x})} + \frac{e^{{x}*{2}}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} + \frac{x*2e^{x}e^{x}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} + \frac{xe^{{x}*{2}}*-0sec^{4}(e^{x})}{2ln^{2}{10}tan^{2}(e^{x})} + \frac{xe^{{x}*{2}}*-2sec^{2}(e^{x})(e^{x})sec^{4}(e^{x})}{2ln{10}tan^{3}(e^{x})} + \frac{xe^{{x}*{2}}*4sec^{4}(e^{x})tan(e^{x})e^{x}}{2ln{10}tan^{2}(e^{x})} - \frac{e^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} - \frac{x*2e^{x}e^{x}sec^{2}(e^{x})}{ln{10}} - \frac{xe^{{x}*{2}}*-0sec^{2}(e^{x})}{ln^{2}{10}} - \frac{xe^{{x}*{2}}*2sec^{2}(e^{x})tan(e^{x})e^{x}}{ln{10}} + \frac{e^{x}}{2ln{10}th(e^{x})} + \frac{e^{x}*-0}{2ln^{2}{10}th(e^{x})} + \frac{e^{x}*-(1 - th^{2}(e^{x}))e^{x}}{2ln{10}th^{2}(e^{x})} - \frac{e^{x}th(e^{x})}{2ln{10}} - \frac{e^{x}*-0th(e^{x})}{2ln^{2}{10}} - \frac{e^{x}(1 - th^{2}(e^{x}))e^{x}}{2ln{10}} + \frac{e^{x}}{4ln{10}th(e^{x})} + \frac{xe^{x}}{4ln{10}th(e^{x})} + \frac{xe^{x}*-0}{4ln^{2}{10}th(e^{x})} + \frac{xe^{x}*-(1 - th^{2}(e^{x}))e^{x}}{4ln{10}th^{2}(e^{x})} - \frac{e^{{x}*{2}}}{4ln{10}th^{2}(e^{x})} - \frac{x*2e^{x}e^{x}}{4ln{10}th^{2}(e^{x})} - \frac{xe^{{x}*{2}}*-0}{4ln^{2}{10}th^{2}(e^{x})} - \frac{xe^{{x}*{2}}*-2(1 - th^{2}(e^{x}))e^{x}}{4ln{10}th^{3}(e^{x})} - \frac{e^{x}th(e^{x})}{4ln{10}} - \frac{xe^{x}th(e^{x})}{4ln{10}} - \frac{xe^{x}*-0th(e^{x})}{4ln^{2}{10}} - \frac{xe^{x}(1 - th^{2}(e^{x}))e^{x}}{4ln{10}} + \frac{e^{{x}*{2}}th^{2}(e^{x})}{4ln{10}} + \frac{x*2e^{x}e^{x}th^{2}(e^{x})}{4ln{10}} + \frac{xe^{{x}*{2}}*-0th^{2}(e^{x})}{4ln^{2}{10}} + \frac{xe^{{x}*{2}}*2th(e^{x})(1 - th^{2}(e^{x}))e^{x}}{4ln{10}} + ({\frac{1}{2}}^{e^{x}}((e^{x})ln(\frac{1}{2}) + \frac{(e^{x})(0)}{(\frac{1}{2})}))e^{{x}*{2}}ln^{2}(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}*2e^{x}e^{x}ln^{2}(\frac{1}{2}) + \frac{{\frac{1}{2}}^{e^{x}}e^{{x}*{2}}*2ln(\frac{1}{2})*0}{(\frac{1}{2})} + ({\frac{1}{2}}^{e^{x}}((e^{x})ln(\frac{1}{2}) + \frac{(e^{x})(0)}{(\frac{1}{2})}))e^{x}ln(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2}) + \frac{{\frac{1}{2}}^{e^{x}}e^{x}*0}{(\frac{1}{2})}\\=&\frac{-3e^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} + \frac{3e^{{x}*{2}}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{3e^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} + \frac{3xe^{{x}*{2}}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{3xe^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} - \frac{xe^{{x}*{3}}sec^{6}(e^{x})}{ln{10}tan^{3}(e^{x})} + \frac{2xe^{{x}*{3}}sec^{4}(e^{x})}{ln{10}tan(e^{x})} - \frac{2xe^{{x}*{3}}tan(e^{x})sec^{2}(e^{x})}{ln{10}} + \frac{3e^{x}}{4ln{10}th(e^{x})} - \frac{3e^{{x}*{2}}}{4ln{10}th^{2}(e^{x})} - \frac{3e^{x}th(e^{x})}{4ln{10}} + \frac{3e^{{x}*{2}}th^{2}(e^{x})}{4ln{10}} + \frac{xe^{x}}{4ln{10}th(e^{x})} - \frac{3xe^{{x}*{2}}}{4ln{10}th^{2}(e^{x})} + \frac{xe^{{x}*{3}}}{2ln{10}th^{3}(e^{x})} - \frac{xe^{{x}*{3}}}{2ln{10}th(e^{x})} - \frac{xe^{x}th(e^{x})}{4ln{10}} + \frac{xe^{{x}*{3}}th(e^{x})}{2ln{10}} - \frac{xe^{{x}*{3}}th^{3}(e^{x})}{2ln{10}} + \frac{3xe^{{x}*{2}}th^{2}(e^{x})}{4ln{10}} + {\frac{1}{2}}^{e^{x}}e^{{x}*{3}}ln^{3}(\frac{1}{2}) + 3 * {\frac{1}{2}}^{e^{x}}e^{{x}*{2}}ln^{2}(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2})\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3e^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} + \frac{3e^{{x}*{2}}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{3e^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} + \frac{3xe^{{x}*{2}}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{3xe^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} - \frac{xe^{{x}*{3}}sec^{6}(e^{x})}{ln{10}tan^{3}(e^{x})} + \frac{2xe^{{x}*{3}}sec^{4}(e^{x})}{ln{10}tan(e^{x})} - \frac{2xe^{{x}*{3}}tan(e^{x})sec^{2}(e^{x})}{ln{10}} + \frac{3e^{x}}{4ln{10}th(e^{x})} - \frac{3e^{{x}*{2}}}{4ln{10}th^{2}(e^{x})} - \frac{3e^{x}th(e^{x})}{4ln{10}} + \frac{3e^{{x}*{2}}th^{2}(e^{x})}{4ln{10}} + \frac{xe^{x}}{4ln{10}th(e^{x})} - \frac{3xe^{{x}*{2}}}{4ln{10}th^{2}(e^{x})} + \frac{xe^{{x}*{3}}}{2ln{10}th^{3}(e^{x})} - \frac{xe^{{x}*{3}}}{2ln{10}th(e^{x})} - \frac{xe^{x}th(e^{x})}{4ln{10}} + \frac{xe^{{x}*{3}}th(e^{x})}{2ln{10}} - \frac{xe^{{x}*{3}}th^{3}(e^{x})}{2ln{10}} + \frac{3xe^{{x}*{2}}th^{2}(e^{x})}{4ln{10}} + {\frac{1}{2}}^{e^{x}}e^{{x}*{3}}ln^{3}(\frac{1}{2}) + 3 * {\frac{1}{2}}^{e^{x}}e^{{x}*{2}}ln^{2}(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2})\right)}{dx}\\=&\frac{-3e^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} - \frac{3e^{x}*-0sec^{2}(e^{x})}{2ln^{2}{10}tan(e^{x})} - \frac{3e^{x}*-sec^{2}(e^{x})(e^{x})sec^{2}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{3e^{x}*2sec^{2}(e^{x})tan(e^{x})e^{x}}{2ln{10}tan(e^{x})} + \frac{3*2e^{x}e^{x}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} + \frac{3e^{{x}*{2}}*-0sec^{4}(e^{x})}{2ln^{2}{10}tan^{2}(e^{x})} + \frac{3e^{{x}*{2}}*-2sec^{2}(e^{x})(e^{x})sec^{4}(e^{x})}{2ln{10}tan^{3}(e^{x})} + \frac{3e^{{x}*{2}}*4sec^{4}(e^{x})tan(e^{x})e^{x}}{2ln{10}tan^{2}(e^{x})} - \frac{3*2e^{x}e^{x}sec^{2}(e^{x})}{ln{10}} - \frac{3e^{{x}*{2}}*-0sec^{2}(e^{x})}{ln^{2}{10}} - \frac{3e^{{x}*{2}}*2sec^{2}(e^{x})tan(e^{x})e^{x}}{ln{10}} - \frac{e^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} - \frac{xe^{x}*-0sec^{2}(e^{x})}{2ln^{2}{10}tan(e^{x})} - \frac{xe^{x}*-sec^{2}(e^{x})(e^{x})sec^{2}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{xe^{x}*2sec^{2}(e^{x})tan(e^{x})e^{x}}{2ln{10}tan(e^{x})} + \frac{3e^{{x}*{2}}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} + \frac{3x*2e^{x}e^{x}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} + \frac{3xe^{{x}*{2}}*-0sec^{4}(e^{x})}{2ln^{2}{10}tan^{2}(e^{x})} + \frac{3xe^{{x}*{2}}*-2sec^{2}(e^{x})(e^{x})sec^{4}(e^{x})}{2ln{10}tan^{3}(e^{x})} + \frac{3xe^{{x}*{2}}*4sec^{4}(e^{x})tan(e^{x})e^{x}}{2ln{10}tan^{2}(e^{x})} - \frac{3e^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} - \frac{3x*2e^{x}e^{x}sec^{2}(e^{x})}{ln{10}} - \frac{3xe^{{x}*{2}}*-0sec^{2}(e^{x})}{ln^{2}{10}} - \frac{3xe^{{x}*{2}}*2sec^{2}(e^{x})tan(e^{x})e^{x}}{ln{10}} - \frac{e^{{x}*{3}}sec^{6}(e^{x})}{ln{10}tan^{3}(e^{x})} - \frac{x*3e^{{x}*{2}}e^{x}sec^{6}(e^{x})}{ln{10}tan^{3}(e^{x})} - \frac{xe^{{x}*{3}}*-0sec^{6}(e^{x})}{ln^{2}{10}tan^{3}(e^{x})} - \frac{xe^{{x}*{3}}*-3sec^{2}(e^{x})(e^{x})sec^{6}(e^{x})}{ln{10}tan^{4}(e^{x})} - \frac{xe^{{x}*{3}}*6sec^{6}(e^{x})tan(e^{x})e^{x}}{ln{10}tan^{3}(e^{x})} + \frac{2e^{{x}*{3}}sec^{4}(e^{x})}{ln{10}tan(e^{x})} + \frac{2x*3e^{{x}*{2}}e^{x}sec^{4}(e^{x})}{ln{10}tan(e^{x})} + \frac{2xe^{{x}*{3}}*-0sec^{4}(e^{x})}{ln^{2}{10}tan(e^{x})} + \frac{2xe^{{x}*{3}}*-sec^{2}(e^{x})(e^{x})sec^{4}(e^{x})}{ln{10}tan^{2}(e^{x})} + \frac{2xe^{{x}*{3}}*4sec^{4}(e^{x})tan(e^{x})e^{x}}{ln{10}tan(e^{x})} - \frac{2e^{{x}*{3}}tan(e^{x})sec^{2}(e^{x})}{ln{10}} - \frac{2x*3e^{{x}*{2}}e^{x}tan(e^{x})sec^{2}(e^{x})}{ln{10}} - \frac{2xe^{{x}*{3}}*-0tan(e^{x})sec^{2}(e^{x})}{ln^{2}{10}} - \frac{2xe^{{x}*{3}}sec^{2}(e^{x})(e^{x})sec^{2}(e^{x})}{ln{10}} - \frac{2xe^{{x}*{3}}tan(e^{x})*2sec^{2}(e^{x})tan(e^{x})e^{x}}{ln{10}} + \frac{3e^{x}}{4ln{10}th(e^{x})} + \frac{3e^{x}*-0}{4ln^{2}{10}th(e^{x})} + \frac{3e^{x}*-(1 - th^{2}(e^{x}))e^{x}}{4ln{10}th^{2}(e^{x})} - \frac{3*2e^{x}e^{x}}{4ln{10}th^{2}(e^{x})} - \frac{3e^{{x}*{2}}*-0}{4ln^{2}{10}th^{2}(e^{x})} - \frac{3e^{{x}*{2}}*-2(1 - th^{2}(e^{x}))e^{x}}{4ln{10}th^{3}(e^{x})} - \frac{3e^{x}th(e^{x})}{4ln{10}} - \frac{3e^{x}*-0th(e^{x})}{4ln^{2}{10}} - \frac{3e^{x}(1 - th^{2}(e^{x}))e^{x}}{4ln{10}} + \frac{3*2e^{x}e^{x}th^{2}(e^{x})}{4ln{10}} + \frac{3e^{{x}*{2}}*-0th^{2}(e^{x})}{4ln^{2}{10}} + \frac{3e^{{x}*{2}}*2th(e^{x})(1 - th^{2}(e^{x}))e^{x}}{4ln{10}} + \frac{e^{x}}{4ln{10}th(e^{x})} + \frac{xe^{x}}{4ln{10}th(e^{x})} + \frac{xe^{x}*-0}{4ln^{2}{10}th(e^{x})} + \frac{xe^{x}*-(1 - th^{2}(e^{x}))e^{x}}{4ln{10}th^{2}(e^{x})} - \frac{3e^{{x}*{2}}}{4ln{10}th^{2}(e^{x})} - \frac{3x*2e^{x}e^{x}}{4ln{10}th^{2}(e^{x})} - \frac{3xe^{{x}*{2}}*-0}{4ln^{2}{10}th^{2}(e^{x})} - \frac{3xe^{{x}*{2}}*-2(1 - th^{2}(e^{x}))e^{x}}{4ln{10}th^{3}(e^{x})} + \frac{e^{{x}*{3}}}{2ln{10}th^{3}(e^{x})} + \frac{x*3e^{{x}*{2}}e^{x}}{2ln{10}th^{3}(e^{x})} + \frac{xe^{{x}*{3}}*-0}{2ln^{2}{10}th^{3}(e^{x})} + \frac{xe^{{x}*{3}}*-3(1 - th^{2}(e^{x}))e^{x}}{2ln{10}th^{4}(e^{x})} - \frac{e^{{x}*{3}}}{2ln{10}th(e^{x})} - \frac{x*3e^{{x}*{2}}e^{x}}{2ln{10}th(e^{x})} - \frac{xe^{{x}*{3}}*-0}{2ln^{2}{10}th(e^{x})} - \frac{xe^{{x}*{3}}*-(1 - th^{2}(e^{x}))e^{x}}{2ln{10}th^{2}(e^{x})} - \frac{e^{x}th(e^{x})}{4ln{10}} - \frac{xe^{x}th(e^{x})}{4ln{10}} - \frac{xe^{x}*-0th(e^{x})}{4ln^{2}{10}} - \frac{xe^{x}(1 - th^{2}(e^{x}))e^{x}}{4ln{10}} + \frac{e^{{x}*{3}}th(e^{x})}{2ln{10}} + \frac{x*3e^{{x}*{2}}e^{x}th(e^{x})}{2ln{10}} + \frac{xe^{{x}*{3}}*-0th(e^{x})}{2ln^{2}{10}} + \frac{xe^{{x}*{3}}(1 - th^{2}(e^{x}))e^{x}}{2ln{10}} - \frac{e^{{x}*{3}}th^{3}(e^{x})}{2ln{10}} - \frac{x*3e^{{x}*{2}}e^{x}th^{3}(e^{x})}{2ln{10}} - \frac{xe^{{x}*{3}}*-0th^{3}(e^{x})}{2ln^{2}{10}} - \frac{xe^{{x}*{3}}*3th^{2}(e^{x})(1 - th^{2}(e^{x}))e^{x}}{2ln{10}} + \frac{3e^{{x}*{2}}th^{2}(e^{x})}{4ln{10}} + \frac{3x*2e^{x}e^{x}th^{2}(e^{x})}{4ln{10}} + \frac{3xe^{{x}*{2}}*-0th^{2}(e^{x})}{4ln^{2}{10}} + \frac{3xe^{{x}*{2}}*2th(e^{x})(1 - th^{2}(e^{x}))e^{x}}{4ln{10}} + ({\frac{1}{2}}^{e^{x}}((e^{x})ln(\frac{1}{2}) + \frac{(e^{x})(0)}{(\frac{1}{2})}))e^{{x}*{3}}ln^{3}(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}*3e^{{x}*{2}}e^{x}ln^{3}(\frac{1}{2}) + \frac{{\frac{1}{2}}^{e^{x}}e^{{x}*{3}}*3ln^{2}(\frac{1}{2})*0}{(\frac{1}{2})} + 3({\frac{1}{2}}^{e^{x}}((e^{x})ln(\frac{1}{2}) + \frac{(e^{x})(0)}{(\frac{1}{2})}))e^{{x}*{2}}ln^{2}(\frac{1}{2}) + 3 * {\frac{1}{2}}^{e^{x}}*2e^{x}e^{x}ln^{2}(\frac{1}{2}) + \frac{3 * {\frac{1}{2}}^{e^{x}}e^{{x}*{2}}*2ln(\frac{1}{2})*0}{(\frac{1}{2})} + ({\frac{1}{2}}^{e^{x}}((e^{x})ln(\frac{1}{2}) + \frac{(e^{x})(0)}{(\frac{1}{2})}))e^{x}ln(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2}) + \frac{{\frac{1}{2}}^{e^{x}}e^{x}*0}{(\frac{1}{2})}\\=&\frac{-2e^{x}sec^{2}(e^{x})}{ln{10}tan(e^{x})} + \frac{6e^{{x}*{2}}sec^{4}(e^{x})}{ln{10}tan^{2}(e^{x})} - \frac{12e^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} - \frac{4e^{{x}*{3}}sec^{6}(e^{x})}{ln{10}tan^{3}(e^{x})} + \frac{8e^{{x}*{3}}sec^{4}(e^{x})}{ln{10}tan(e^{x})} - \frac{8e^{{x}*{3}}tan(e^{x})sec^{2}(e^{x})}{ln{10}} - \frac{xe^{x}sec^{2}(e^{x})}{2ln{10}tan(e^{x})} + \frac{7xe^{{x}*{2}}sec^{4}(e^{x})}{2ln{10}tan^{2}(e^{x})} - \frac{7xe^{{x}*{2}}sec^{2}(e^{x})}{ln{10}} + \frac{3xe^{{x}*{4}}sec^{8}(e^{x})}{ln{10}tan^{4}(e^{x})} - \frac{6xe^{{x}*{3}}sec^{6}(e^{x})}{ln{10}tan^{3}(e^{x})} + \frac{12xe^{{x}*{3}}sec^{4}(e^{x})}{ln{10}tan(e^{x})} + \frac{6xe^{{x}*{4}}sec^{4}(e^{x})}{ln{10}} - \frac{8xe^{{x}*{4}}sec^{6}(e^{x})}{ln{10}tan^{2}(e^{x})} - \frac{12xe^{{x}*{3}}tan(e^{x})sec^{2}(e^{x})}{ln{10}} - \frac{4xe^{{x}*{4}}tan^{2}(e^{x})sec^{2}(e^{x})}{ln{10}} + \frac{e^{x}}{ln{10}th(e^{x})} - \frac{3e^{{x}*{2}}}{ln{10}th^{2}(e^{x})} + \frac{2e^{{x}*{3}}}{ln{10}th^{3}(e^{x})} - \frac{2e^{{x}*{3}}}{ln{10}th(e^{x})} - \frac{e^{x}th(e^{x})}{ln{10}} + \frac{2e^{{x}*{3}}th(e^{x})}{ln{10}} - \frac{2e^{{x}*{3}}th^{3}(e^{x})}{ln{10}} + \frac{3e^{{x}*{2}}th^{2}(e^{x})}{ln{10}} + \frac{xe^{x}}{4ln{10}th(e^{x})} - \frac{7xe^{{x}*{2}}}{4ln{10}th^{2}(e^{x})} + \frac{3xe^{{x}*{3}}}{ln{10}th^{3}(e^{x})} - \frac{3xe^{{x}*{3}}}{ln{10}th(e^{x})} - \frac{3xe^{{x}*{4}}}{2ln{10}th^{4}(e^{x})} + \frac{2xe^{{x}*{4}}}{ln{10}th^{2}(e^{x})} - \frac{xe^{x}th(e^{x})}{4ln{10}} - \frac{2xe^{{x}*{4}}th^{2}(e^{x})}{ln{10}} + \frac{3xe^{{x}*{4}}th^{4}(e^{x})}{2ln{10}} + \frac{3xe^{{x}*{3}}th(e^{x})}{ln{10}} - \frac{3xe^{{x}*{3}}th^{3}(e^{x})}{ln{10}} + \frac{7xe^{{x}*{2}}th^{2}(e^{x})}{4ln{10}} + {\frac{1}{2}}^{e^{x}}e^{{x}*{4}}ln^{4}(\frac{1}{2}) + 6 * {\frac{1}{2}}^{e^{x}}e^{{x}*{3}}ln^{3}(\frac{1}{2}) + 7 * {\frac{1}{2}}^{e^{x}}e^{{x}*{2}}ln^{2}(\frac{1}{2}) + {\frac{1}{2}}^{e^{x}}e^{x}ln(\frac{1}{2})\\ \end{split}\end{equation} \]