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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}\right)}{dx}\\=&e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})\\=&\frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)ln{10}} + \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)ln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)ln{10}} + \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)ln{10}}\right)}{dx}\\=&\frac{3(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} + \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x - 1)ln{10}} + \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x - 1)ln^{2}{10}} + \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} + \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x + 1)ln{10}} + \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x + 1)ln^{2}{10}}\\=&\frac{-3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{2}ln{10}} + \frac{9e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)ln^{2}{10}} - \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{2}ln{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}ln^{2}{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{2}ln{10}} + \frac{9e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)ln^{2}{10}} - \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{2}ln{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{-3(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} - \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x - 1)^{2}ln{10}} - \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x - 1)^{2}ln^{2}{10}} + \frac{9(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25ln^{2}{10}} + \frac{9e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)^{2}ln^{2}{10}} + \frac{9e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)^{2}ln^{3}{10}} + \frac{6(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)ln^{2}{10}} + \frac{6(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)(x - 1)ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)(x - 1)ln^{3}{10}} - \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} - \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x + 1)^{2}ln{10}} - \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x + 1)^{2}ln^{2}{10}} + \frac{6(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)ln^{2}{10}} + \frac{6(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)(x + 1)ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)(x + 1)ln^{3}{10}} + \frac{4(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)^{2}ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)^{2}ln^{3}{10}}\\=&\frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{3}ln{10}} - \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{3}ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)^{2}ln^{2}{10}} + \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{3}ln^{3}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)(x - 1)^{2}ln^{3}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}(x - 1)ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}(x + 1)ln^{2}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}(x - 1)ln^{3}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)^{2}ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{3}ln{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{3}ln^{2}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)(x + 1)^{2}ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}(x + 1)ln^{3}{10}} + \frac{8e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{3}ln^{3}{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{3}ln{10}} - \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{3}ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)^{2}ln^{2}{10}} + \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{3}ln^{3}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)(x - 1)^{2}ln^{3}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}(x - 1)ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}(x + 1)ln^{2}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}(x - 1)ln^{3}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)^{2}ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{3}ln{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{3}ln^{2}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)(x + 1)^{2}ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}(x + 1)ln^{3}{10}} + \frac{8e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{6(\frac{-3(1 + 0)}{(x - 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x - 1)^{3}ln{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x - 1)^{3}ln^{2}{10}} - \frac{27(\frac{-3(1 + 0)}{(x - 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25ln^{2}{10}} - \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)^{3}ln^{2}{10}} - \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)^{3}ln^{3}{10}} - \frac{6(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}ln^{2}{10}} - \frac{6(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)(x - 1)^{2}ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)(x - 1)^{2}ln^{3}{10}} + \frac{27(\frac{-3(1 + 0)}{(x - 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125ln^{3}{10}} + \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x - 1)^{3}ln^{3}{10}} + \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x - 1)^{3}ln^{4}{10}} + \frac{36(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}ln^{3}{10}} + \frac{36(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)ln^{3}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x + 1)(x - 1)^{2}ln^{3}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x + 1)(x - 1)^{2}ln^{4}{10}} - \frac{12(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)ln^{2}{10}} - \frac{12(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)^{2}(x - 1)ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)^{2}(x - 1)ln^{3}{10}} - \frac{12(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)ln^{2}{10}} - \frac{12(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)^{2}(x + 1)ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)^{2}(x + 1)ln^{3}{10}} + \frac{12(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)ln^{3}{10}} + \frac{12(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}ln^{3}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x + 1)^{2}(x - 1)ln^{3}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x + 1)^{2}(x - 1)ln^{4}{10}} - \frac{6(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}ln^{2}{10}} - \frac{6(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)(x + 1)^{2}ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)(x + 1)^{2}ln^{3}{10}} + \frac{4(\frac{-3(1 + 0)}{(x + 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x + 1)^{3}ln{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x + 1)^{3}ln^{2}{10}} - \frac{12(\frac{-3(1 + 0)}{(x + 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)^{3}ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)^{3}ln^{3}{10}} + \frac{24(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}ln^{3}{10}} + \frac{24(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)ln^{3}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x - 1)(x + 1)^{2}ln^{3}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x - 1)(x + 1)^{2}ln^{4}{10}} + \frac{18(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)ln^{3}{10}} + \frac{18(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x - 1)^{2}(x + 1)ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x - 1)^{2}(x + 1)ln^{4}{10}} + \frac{8(\frac{-3(1 + 0)}{(x + 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125ln^{3}{10}} + \frac{8e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x + 1)^{3}ln^{3}{10}} + \frac{8e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x + 1)^{3}ln^{4}{10}}\\=&\frac{-18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{4}ln{10}} + \frac{99e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{4}ln^{2}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)^{3}ln^{2}{10}} - \frac{162e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{4}ln^{3}{10}} - \frac{72e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)(x - 1)^{3}ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}(x - 1)^{2}ln^{2}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{3}(x + 1)ln^{2}{10}} - \frac{96e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}(x - 1)^{2}ln^{3}{10}} + \frac{81e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x - 1)^{4}ln^{4}{10}} + \frac{162e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x + 1)(x - 1)^{3}ln^{4}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)^{3}ln^{2}{10}} - \frac{144e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{3}(x + 1)ln^{3}{10}} + \frac{108e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x + 1)^{2}(x - 1)^{2}ln^{4}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{3}(x - 1)ln^{2}{10}} - \frac{96e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{3}(x - 1)ln^{3}{10}} + \frac{44e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{4}ln^{2}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}(x + 1)^{2}ln^{2}{10}} - \frac{84e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}(x + 1)^{2}ln^{3}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x + 1)^{3}(x - 1)ln^{4}{10}} - \frac{48e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)(x + 1)^{3}ln^{3}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{4}ln{10}} - \frac{48e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{4}ln^{3}{10}} + \frac{72e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x - 1)(x + 1)^{3}ln^{4}{10}} + \frac{16e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x + 1)^{4}ln^{4}{10}} + \frac{108e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x - 1)^{2}(x + 1)^{2}ln^{4}{10}} + \frac{54e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x - 1)^{3}(x + 1)ln^{4}{10}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}\right)}{dx}\\=&e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})\\=&\frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)ln{10}} + \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)ln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)ln{10}} + \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)ln{10}}\right)}{dx}\\=&\frac{3(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} + \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x - 1)ln{10}} + \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x - 1)ln^{2}{10}} + \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} + \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x + 1)ln{10}} + \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x + 1)ln^{2}{10}}\\=&\frac{-3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{2}ln{10}} + \frac{9e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)ln^{2}{10}} - \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{2}ln{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}ln^{2}{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{2}ln{10}} + \frac{9e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)ln^{2}{10}} - \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{2}ln{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{-3(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} - \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x - 1)^{2}ln{10}} - \frac{3e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x - 1)^{2}ln^{2}{10}} + \frac{9(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25ln^{2}{10}} + \frac{9e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)^{2}ln^{2}{10}} + \frac{9e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)^{2}ln^{3}{10}} + \frac{6(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)ln^{2}{10}} + \frac{6(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)(x - 1)ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)(x - 1)ln^{3}{10}} - \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} - \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x + 1)^{2}ln{10}} - \frac{2e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x + 1)^{2}ln^{2}{10}} + \frac{6(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)ln^{2}{10}} + \frac{6(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)(x + 1)ln^{2}{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)(x + 1)ln^{3}{10}} + \frac{4(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)^{2}ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)^{2}ln^{3}{10}}\\=&\frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{3}ln{10}} - \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{3}ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)^{2}ln^{2}{10}} + \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{3}ln^{3}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)(x - 1)^{2}ln^{3}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}(x - 1)ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}(x + 1)ln^{2}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}(x - 1)ln^{3}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)^{2}ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{3}ln{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{3}ln^{2}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)(x + 1)^{2}ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}(x + 1)ln^{3}{10}} + \frac{8e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{3}ln^{3}{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{3}ln{10}} - \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{3}ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)^{2}ln^{2}{10}} + \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{3}ln^{3}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)(x - 1)^{2}ln^{3}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}(x - 1)ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}(x + 1)ln^{2}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}(x - 1)ln^{3}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)^{2}ln^{2}{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{3}ln{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{3}ln^{2}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)(x + 1)^{2}ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}(x + 1)ln^{3}{10}} + \frac{8e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{6(\frac{-3(1 + 0)}{(x - 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x - 1)^{3}ln{10}} + \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x - 1)^{3}ln^{2}{10}} - \frac{27(\frac{-3(1 + 0)}{(x - 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25ln^{2}{10}} - \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)^{3}ln^{2}{10}} - \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)^{3}ln^{3}{10}} - \frac{6(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}ln^{2}{10}} - \frac{6(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)(x - 1)^{2}ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)(x - 1)^{2}ln^{3}{10}} + \frac{27(\frac{-3(1 + 0)}{(x - 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125ln^{3}{10}} + \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x - 1)^{3}ln^{3}{10}} + \frac{27e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x - 1)^{3}ln^{4}{10}} + \frac{36(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}ln^{3}{10}} + \frac{36(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)ln^{3}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x + 1)(x - 1)^{2}ln^{3}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x + 1)(x - 1)^{2}ln^{4}{10}} - \frac{12(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)ln^{2}{10}} - \frac{12(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)^{2}(x - 1)ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)^{2}(x - 1)ln^{3}{10}} - \frac{12(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)ln^{2}{10}} - \frac{12(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)^{2}(x + 1)ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)^{2}(x + 1)ln^{3}{10}} + \frac{12(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)ln^{3}{10}} + \frac{12(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}ln^{3}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x + 1)^{2}(x - 1)ln^{3}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x + 1)^{2}(x - 1)ln^{4}{10}} - \frac{6(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}ln^{2}{10}} - \frac{6(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x - 1)(x + 1)^{2}ln^{2}{10}} - \frac{6e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x - 1)(x + 1)^{2}ln^{3}{10}} + \frac{4(\frac{-3(1 + 0)}{(x + 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5ln{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{5(x + 1)^{3}ln{10}} + \frac{4e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-0}{5(x + 1)^{3}ln^{2}{10}} - \frac{12(\frac{-3(1 + 0)}{(x + 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{25(x + 1)^{3}ln^{2}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-2*0}{25(x + 1)^{3}ln^{3}{10}} + \frac{24(\frac{-(1 + 0)}{(x - 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}ln^{3}{10}} + \frac{24(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)ln^{3}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x - 1)(x + 1)^{2}ln^{3}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x - 1)(x + 1)^{2}ln^{4}{10}} + \frac{18(\frac{-2(1 + 0)}{(x - 1)^{3}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)ln^{3}{10}} + \frac{18(\frac{-(1 + 0)}{(x + 1)^{2}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x - 1)^{2}(x + 1)ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x - 1)^{2}(x + 1)ln^{4}{10}} + \frac{8(\frac{-3(1 + 0)}{(x + 1)^{4}})e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125ln^{3}{10}} + \frac{8e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}(\frac{\frac{3}{5}(1 + 0)}{ln{10}(x - 1)} + \frac{\frac{2}{5}(1 + 0)}{ln{10}(x + 1)})}{125(x + 1)^{3}ln^{3}{10}} + \frac{8e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}*-3*0}{125(x + 1)^{3}ln^{4}{10}}\\=&\frac{-18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x - 1)^{4}ln{10}} + \frac{99e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{4}ln^{2}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)(x - 1)^{3}ln^{2}{10}} - \frac{162e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{4}ln^{3}{10}} - \frac{72e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)(x - 1)^{3}ln^{3}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{2}(x - 1)^{2}ln^{2}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{3}(x + 1)ln^{2}{10}} - \frac{96e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{2}(x - 1)^{2}ln^{3}{10}} + \frac{81e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x - 1)^{4}ln^{4}{10}} + \frac{162e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x + 1)(x - 1)^{3}ln^{4}{10}} + \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)(x + 1)^{3}ln^{2}{10}} - \frac{144e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{3}(x + 1)ln^{3}{10}} + \frac{108e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x + 1)^{2}(x - 1)^{2}ln^{4}{10}} + \frac{36e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{3}(x - 1)ln^{2}{10}} - \frac{96e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{3}(x - 1)ln^{3}{10}} + \frac{44e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x + 1)^{4}ln^{2}{10}} + \frac{18e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{25(x - 1)^{2}(x + 1)^{2}ln^{2}{10}} - \frac{84e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)^{2}(x + 1)^{2}ln^{3}{10}} + \frac{24e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x + 1)^{3}(x - 1)ln^{4}{10}} - \frac{48e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x - 1)(x + 1)^{3}ln^{3}{10}} - \frac{12e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{5(x + 1)^{4}ln{10}} - \frac{48e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{125(x + 1)^{4}ln^{3}{10}} + \frac{72e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x - 1)(x + 1)^{3}ln^{4}{10}} + \frac{16e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x + 1)^{4}ln^{4}{10}} + \frac{108e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x - 1)^{2}(x + 1)^{2}ln^{4}{10}} + \frac{54e^{\frac{3}{5}lg(x - 1) + \frac{2}{5}lg(x + 1)}}{625(x - 1)^{3}(x + 1)ln^{4}{10}}\\ \end{split}\end{equation} \]