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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{({e}^{2}x - {(x + 1)}^{2})}{(ln(x + 1) - x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{xe^{2}}{(ln(x + 1) - x)} - \frac{x^{2}}{(ln(x + 1) - x)} - \frac{2x}{(ln(x + 1) - x)} - \frac{1}{(ln(x + 1) - x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{xe^{2}}{(ln(x + 1) - x)} - \frac{x^{2}}{(ln(x + 1) - x)} - \frac{2x}{(ln(x + 1) - x)} - \frac{1}{(ln(x + 1) - x)}\right)}{dx}\\=&(\frac{-(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{2}})xe^{2} + \frac{e^{2}}{(ln(x + 1) - x)} + \frac{x*2e*0}{(ln(x + 1) - x)} - (\frac{-(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{2}})x^{2} - \frac{2x}{(ln(x + 1) - x)} - 2(\frac{-(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{2}})x - \frac{2}{(ln(x + 1) - x)} - (\frac{-(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{2}})\\=&\frac{-xe^{2}}{(ln(x + 1) - x)^{2}(x + 1)} + \frac{xe^{2}}{(ln(x + 1) - x)^{2}} + \frac{e^{2}}{(ln(x + 1) - x)} + \frac{x^{2}}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{x^{2}}{(ln(x + 1) - x)^{2}} - \frac{2x}{(ln(x + 1) - x)} + \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{2x}{(ln(x + 1) - x)^{2}} + \frac{1}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{2}{(ln(x + 1) - x)} - \frac{1}{(ln(x + 1) - x)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-xe^{2}}{(ln(x + 1) - x)^{2}(x + 1)} + \frac{xe^{2}}{(ln(x + 1) - x)^{2}} + \frac{e^{2}}{(ln(x + 1) - x)} + \frac{x^{2}}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{x^{2}}{(ln(x + 1) - x)^{2}} - \frac{2x}{(ln(x + 1) - x)} + \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{2x}{(ln(x + 1) - x)^{2}} + \frac{1}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{2}{(ln(x + 1) - x)} - \frac{1}{(ln(x + 1) - x)^{2}}\right)}{dx}\\=&\frac{-(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})xe^{2}}{(x + 1)} - \frac{(\frac{-(1 + 0)}{(x + 1)^{2}})xe^{2}}{(ln(x + 1) - x)^{2}} - \frac{e^{2}}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{x*2e*0}{(ln(x + 1) - x)^{2}(x + 1)} + (\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})xe^{2} + \frac{e^{2}}{(ln(x + 1) - x)^{2}} + \frac{x*2e*0}{(ln(x + 1) - x)^{2}} + (\frac{-(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{2}})e^{2} + \frac{2e*0}{(ln(x + 1) - x)} + \frac{(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x^{2}}{(x + 1)} + \frac{(\frac{-(1 + 0)}{(x + 1)^{2}})x^{2}}{(ln(x + 1) - x)^{2}} + \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)} - (\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x^{2} - \frac{2x}{(ln(x + 1) - x)^{2}} - 2(\frac{-(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{2}})x - \frac{2}{(ln(x + 1) - x)} + \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x}{(x + 1)} + \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})x}{(ln(x + 1) - x)^{2}} + \frac{2}{(ln(x + 1) - x)^{2}(x + 1)} - 2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x - \frac{2}{(ln(x + 1) - x)^{2}} + \frac{(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})}{(x + 1)} + \frac{(\frac{-(1 + 0)}{(x + 1)^{2}})}{(ln(x + 1) - x)^{2}} - 2(\frac{-(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{2}}) - (\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})\\=&\frac{2xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{4xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)} + \frac{xe^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{2}} - \frac{2e^{2}}{(ln(x + 1) - x)^{2}(x + 1)} + \frac{2xe^{2}}{(ln(x + 1) - x)^{3}} + \frac{2e^{2}}{(ln(x + 1) - x)^{2}} - \frac{2x^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{4x^{2}}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{x^{2}}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{2x}{(x + 1)(ln(x + 1) - x)^{2}} - \frac{2x^{2}}{(ln(x + 1) - x)^{3}} - \frac{4x}{(ln(x + 1) - x)^{2}} + \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{4x}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{8x}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{4}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{4x}{(ln(x + 1) - x)^{3}} - \frac{2}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{4}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{1}{(ln(x + 1) - x)^{2}(x + 1)^{2}} - \frac{2}{(ln(x + 1) - x)} - \frac{4}{(ln(x + 1) - x)^{2}} - \frac{2}{(ln(x + 1) - x)^{3}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{4xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)} + \frac{xe^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{2}} - \frac{2e^{2}}{(ln(x + 1) - x)^{2}(x + 1)} + \frac{2xe^{2}}{(ln(x + 1) - x)^{3}} + \frac{2e^{2}}{(ln(x + 1) - x)^{2}} - \frac{2x^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{4x^{2}}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{x^{2}}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{2x}{(x + 1)(ln(x + 1) - x)^{2}} - \frac{2x^{2}}{(ln(x + 1) - x)^{3}} - \frac{4x}{(ln(x + 1) - x)^{2}} + \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{4x}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{8x}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{4}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{4x}{(ln(x + 1) - x)^{3}} - \frac{2}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{4}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{1}{(ln(x + 1) - x)^{2}(x + 1)^{2}} - \frac{2}{(ln(x + 1) - x)} - \frac{4}{(ln(x + 1) - x)^{2}} - \frac{2}{(ln(x + 1) - x)^{3}}\right)}{dx}\\=&\frac{2(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})xe^{2}}{(x + 1)^{2}} + \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})xe^{2}}{(ln(x + 1) - x)^{3}} + \frac{2e^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{2x*2e*0}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{4(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})xe^{2}}{(x + 1)} - \frac{4(\frac{-(1 + 0)}{(x + 1)^{2}})xe^{2}}{(ln(x + 1) - x)^{3}} - \frac{4e^{2}}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{4x*2e*0}{(ln(x + 1) - x)^{3}(x + 1)} + \frac{(\frac{-2(1 + 0)}{(x + 1)^{3}})xe^{2}}{(ln(x + 1) - x)^{2}} + \frac{(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})xe^{2}}{(x + 1)^{2}} + \frac{e^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{2}} + \frac{x*2e*0}{(x + 1)^{2}(ln(x + 1) - x)^{2}} - \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})e^{2}}{(x + 1)} - \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})e^{2}}{(ln(x + 1) - x)^{2}} - \frac{2*2e*0}{(ln(x + 1) - x)^{2}(x + 1)} + 2(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})xe^{2} + \frac{2e^{2}}{(ln(x + 1) - x)^{3}} + \frac{2x*2e*0}{(ln(x + 1) - x)^{3}} + 2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})e^{2} + \frac{2*2e*0}{(ln(x + 1) - x)^{2}} - \frac{2(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x^{2}}{(x + 1)^{2}} - \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})x^{2}}{(ln(x + 1) - x)^{3}} - \frac{2*2x}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{4(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x^{2}}{(x + 1)} + \frac{4(\frac{-(1 + 0)}{(x + 1)^{2}})x^{2}}{(ln(x + 1) - x)^{3}} + \frac{4*2x}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x^{2}}{(x + 1)^{2}} - \frac{(\frac{-2(1 + 0)}{(x + 1)^{3}})x^{2}}{(ln(x + 1) - x)^{2}} - \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})x}{(ln(x + 1) - x)^{2}} + \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x}{(x + 1)} + \frac{2}{(x + 1)(ln(x + 1) - x)^{2}} - 2(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x^{2} - \frac{2*2x}{(ln(x + 1) - x)^{3}} - 4(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x - \frac{4}{(ln(x + 1) - x)^{2}} + \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x}{(x + 1)} + \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})x}{(ln(x + 1) - x)^{2}} + \frac{2}{(ln(x + 1) - x)^{2}(x + 1)} - \frac{4(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x}{(x + 1)^{2}} - \frac{4(\frac{-2(1 + 0)}{(x + 1)^{3}})x}{(ln(x + 1) - x)^{3}} - \frac{4}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{8(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x}{(x + 1)} + \frac{8(\frac{-(1 + 0)}{(x + 1)^{2}})x}{(ln(x + 1) - x)^{3}} + \frac{8}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x}{(x + 1)^{2}} - \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})x}{(ln(x + 1) - x)^{2}} - \frac{2}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{4(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})}{(x + 1)} + \frac{4(\frac{-(1 + 0)}{(x + 1)^{2}})}{(ln(x + 1) - x)^{2}} - 4(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x - \frac{4}{(ln(x + 1) - x)^{3}} - \frac{2(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})}{(x + 1)^{2}} - \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(ln(x + 1) - x)^{3}} + \frac{4(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})}{(x + 1)} + \frac{4(\frac{-(1 + 0)}{(x + 1)^{2}})}{(ln(x + 1) - x)^{3}} - \frac{(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})}{(x + 1)^{2}} - \frac{(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(ln(x + 1) - x)^{2}} - 2(\frac{-(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{2}}) - 4(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}}) - 2(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})\\=&\frac{-6xe^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} + \frac{18xe^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} - \frac{4xe^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{3}} + \frac{6e^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{18xe^{2}}{(ln(x + 1) - x)^{4}(x + 1)} + \frac{4xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{12e^{2}}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{2xe^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{2}} - \frac{2xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{2xe^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{e^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{2}} + \frac{2e^{2}}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{6xe^{2}}{(ln(x + 1) - x)^{4}} + \frac{6e^{2}}{(ln(x + 1) - x)^{3}} + \frac{6x^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{18x^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{6x^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{3}} - \frac{4x}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{18x^{2}}{(ln(x + 1) - x)^{4}(x + 1)} - \frac{6x^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{8x}{(x + 1)(ln(x + 1) - x)^{3}} + \frac{2x^{2}}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{4x}{(x + 1)^{2}(ln(x + 1) - x)^{2}} - \frac{20x}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{16x}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{12x}{(ln(x + 1) - x)^{3}} - \frac{6x^{2}}{(ln(x + 1) - x)^{4}} - \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{12x}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{36x}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{12x}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{36x}{(ln(x + 1) - x)^{4}(x + 1)} + \frac{4x}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{6}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{4}{(ln(x + 1) - x)^{2}(x + 1)} + \frac{24}{(ln(x + 1) - x)^{3}(x + 1)} + \frac{2}{(x + 1)(ln(x + 1) - x)^{2}} - \frac{18}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{12x}{(ln(x + 1) - x)^{4}} - \frac{18}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{6}{(ln(x + 1) - x)^{4}(x + 1)^{3}} + \frac{6}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{18}{(ln(x + 1) - x)^{4}(x + 1)} + \frac{2}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{12}{(ln(x + 1) - x)^{3}} - \frac{6}{(ln(x + 1) - x)^{2}} - \frac{6}{(ln(x + 1) - x)^{4}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6xe^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} + \frac{18xe^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} - \frac{4xe^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{3}} + \frac{6e^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{18xe^{2}}{(ln(x + 1) - x)^{4}(x + 1)} + \frac{4xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{12e^{2}}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{2xe^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{2}} - \frac{2xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{2xe^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{e^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{2}} + \frac{2e^{2}}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{6xe^{2}}{(ln(x + 1) - x)^{4}} + \frac{6e^{2}}{(ln(x + 1) - x)^{3}} + \frac{6x^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{18x^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{6x^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{3}} - \frac{4x}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{18x^{2}}{(ln(x + 1) - x)^{4}(x + 1)} - \frac{6x^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{8x}{(x + 1)(ln(x + 1) - x)^{3}} + \frac{2x^{2}}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{4x}{(x + 1)^{2}(ln(x + 1) - x)^{2}} - \frac{20x}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{16x}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{12x}{(ln(x + 1) - x)^{3}} - \frac{6x^{2}}{(ln(x + 1) - x)^{4}} - \frac{2x}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{12x}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{36x}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{12x}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{36x}{(ln(x + 1) - x)^{4}(x + 1)} + \frac{4x}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{6}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{4}{(ln(x + 1) - x)^{2}(x + 1)} + \frac{24}{(ln(x + 1) - x)^{3}(x + 1)} + \frac{2}{(x + 1)(ln(x + 1) - x)^{2}} - \frac{18}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{12x}{(ln(x + 1) - x)^{4}} - \frac{18}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{6}{(ln(x + 1) - x)^{4}(x + 1)^{3}} + \frac{6}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{18}{(ln(x + 1) - x)^{4}(x + 1)} + \frac{2}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{12}{(ln(x + 1) - x)^{3}} - \frac{6}{(ln(x + 1) - x)^{2}} - \frac{6}{(ln(x + 1) - x)^{4}}\right)}{dx}\\=&\frac{-6(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})xe^{2}}{(x + 1)^{3}} - \frac{6(\frac{-3(1 + 0)}{(x + 1)^{4}})xe^{2}}{(ln(x + 1) - x)^{4}} - \frac{6e^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{6x*2e*0}{(ln(x + 1) - x)^{4}(x + 1)^{3}} + \frac{18(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})xe^{2}}{(x + 1)^{2}} + \frac{18(\frac{-2(1 + 0)}{(x + 1)^{3}})xe^{2}}{(ln(x + 1) - x)^{4}} + \frac{18e^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{18x*2e*0}{(ln(x + 1) - x)^{4}(x + 1)^{2}} - \frac{4(\frac{-3(1 + 0)}{(x + 1)^{4}})xe^{2}}{(ln(x + 1) - x)^{3}} - \frac{4(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})xe^{2}}{(x + 1)^{3}} - \frac{4e^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{3}} - \frac{4x*2e*0}{(x + 1)^{3}(ln(x + 1) - x)^{3}} + \frac{6(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})e^{2}}{(x + 1)^{2}} + \frac{6(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{2}}{(ln(x + 1) - x)^{3}} + \frac{6*2e*0}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{18(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})xe^{2}}{(x + 1)} - \frac{18(\frac{-(1 + 0)}{(x + 1)^{2}})xe^{2}}{(ln(x + 1) - x)^{4}} - \frac{18e^{2}}{(ln(x + 1) - x)^{4}(x + 1)} - \frac{18x*2e*0}{(ln(x + 1) - x)^{4}(x + 1)} + \frac{4(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})xe^{2}}{(x + 1)^{2}} + \frac{4(\frac{-2(1 + 0)}{(x + 1)^{3}})xe^{2}}{(ln(x + 1) - x)^{3}} + \frac{4e^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{4x*2e*0}{(ln(x + 1) - x)^{3}(x + 1)^{2}} - \frac{12(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})e^{2}}{(x + 1)} - \frac{12(\frac{-(1 + 0)}{(x + 1)^{2}})e^{2}}{(ln(x + 1) - x)^{3}} - \frac{12*2e*0}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{2(\frac{-3(1 + 0)}{(x + 1)^{4}})xe^{2}}{(ln(x + 1) - x)^{2}} - \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})xe^{2}}{(x + 1)^{3}} - \frac{2e^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{2}} - \frac{2x*2e*0}{(x + 1)^{3}(ln(x + 1) - x)^{2}} - \frac{2(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})xe^{2}}{(x + 1)^{3}} - \frac{2(\frac{-3(1 + 0)}{(x + 1)^{4}})xe^{2}}{(ln(x + 1) - x)^{3}} - \frac{2e^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{3}} - \frac{2x*2e*0}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})xe^{2}}{(ln(x + 1) - x)^{3}} + \frac{2(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})xe^{2}}{(x + 1)^{2}} + \frac{2e^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{2x*2e*0}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{2}}{(ln(x + 1) - x)^{2}} + \frac{(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})e^{2}}{(x + 1)^{2}} + \frac{2e*0}{(x + 1)^{2}(ln(x + 1) - x)^{2}} + \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})e^{2}}{(x + 1)^{2}} + \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})e^{2}}{(ln(x + 1) - x)^{2}} + \frac{2*2e*0}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + 6(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})xe^{2} + \frac{6e^{2}}{(ln(x + 1) - x)^{4}} + \frac{6x*2e*0}{(ln(x + 1) - x)^{4}} + 6(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})e^{2} + \frac{6*2e*0}{(ln(x + 1) - x)^{3}} + \frac{6(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})x^{2}}{(x + 1)^{3}} + \frac{6(\frac{-3(1 + 0)}{(x + 1)^{4}})x^{2}}{(ln(x + 1) - x)^{4}} + \frac{6*2x}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{18(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})x^{2}}{(x + 1)^{2}} - \frac{18(\frac{-2(1 + 0)}{(x + 1)^{3}})x^{2}}{(ln(x + 1) - x)^{4}} - \frac{18*2x}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{6(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x^{2}}{(x + 1)^{3}} + \frac{6(\frac{-3(1 + 0)}{(x + 1)^{4}})x^{2}}{(ln(x + 1) - x)^{3}} + \frac{6*2x}{(ln(x + 1) - x)^{3}(x + 1)^{3}} - \frac{4(\frac{-2(1 + 0)}{(x + 1)^{3}})x}{(ln(x + 1) - x)^{3}} - \frac{4(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x}{(x + 1)^{2}} - \frac{4}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{18(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})x^{2}}{(x + 1)} + \frac{18(\frac{-(1 + 0)}{(x + 1)^{2}})x^{2}}{(ln(x + 1) - x)^{4}} + \frac{18*2x}{(ln(x + 1) - x)^{4}(x + 1)} - \frac{6(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x^{2}}{(x + 1)^{2}} - \frac{6(\frac{-2(1 + 0)}{(x + 1)^{3}})x^{2}}{(ln(x + 1) - x)^{3}} - \frac{6*2x}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{8(\frac{-(1 + 0)}{(x + 1)^{2}})x}{(ln(x + 1) - x)^{3}} + \frac{8(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x}{(x + 1)} + \frac{8}{(x + 1)(ln(x + 1) - x)^{3}} + \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x^{2}}{(x + 1)^{3}} + \frac{2(\frac{-3(1 + 0)}{(x + 1)^{4}})x^{2}}{(ln(x + 1) - x)^{2}} + \frac{2*2x}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{4(\frac{-2(1 + 0)}{(x + 1)^{3}})x}{(ln(x + 1) - x)^{2}} - \frac{4(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x}{(x + 1)^{2}} - \frac{4}{(x + 1)^{2}(ln(x + 1) - x)^{2}} - \frac{20(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x}{(x + 1)^{2}} - \frac{20(\frac{-2(1 + 0)}{(x + 1)^{3}})x}{(ln(x + 1) - x)^{3}} - \frac{20}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{16(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x}{(x + 1)} + \frac{16(\frac{-(1 + 0)}{(x + 1)^{2}})x}{(ln(x + 1) - x)^{3}} + \frac{16}{(ln(x + 1) - x)^{3}(x + 1)} - 12(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x - \frac{12}{(ln(x + 1) - x)^{3}} - 6(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})x^{2} - \frac{6*2x}{(ln(x + 1) - x)^{4}} - \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x}{(x + 1)^{2}} - \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})x}{(ln(x + 1) - x)^{2}} - \frac{2}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{12(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})x}{(x + 1)^{3}} + \frac{12(\frac{-3(1 + 0)}{(x + 1)^{4}})x}{(ln(x + 1) - x)^{4}} + \frac{12}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{36(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})x}{(x + 1)^{2}} - \frac{36(\frac{-2(1 + 0)}{(x + 1)^{3}})x}{(ln(x + 1) - x)^{4}} - \frac{36}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{12(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})x}{(x + 1)^{3}} + \frac{12(\frac{-3(1 + 0)}{(x + 1)^{4}})x}{(ln(x + 1) - x)^{3}} + \frac{12}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{36(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})x}{(x + 1)} + \frac{36(\frac{-(1 + 0)}{(x + 1)^{2}})x}{(ln(x + 1) - x)^{4}} + \frac{36}{(ln(x + 1) - x)^{4}(x + 1)} + \frac{4(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})x}{(x + 1)^{3}} + \frac{4(\frac{-3(1 + 0)}{(x + 1)^{4}})x}{(ln(x + 1) - x)^{2}} + \frac{4}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{6(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})}{(x + 1)^{2}} - \frac{6(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(ln(x + 1) - x)^{2}} + \frac{4(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})}{(x + 1)} + \frac{4(\frac{-(1 + 0)}{(x + 1)^{2}})}{(ln(x + 1) - x)^{2}} + \frac{24(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})}{(x + 1)} + \frac{24(\frac{-(1 + 0)}{(x + 1)^{2}})}{(ln(x + 1) - x)^{3}} + \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})}{(ln(x + 1) - x)^{2}} + \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})}{(x + 1)} - \frac{18(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})}{(x + 1)^{2}} - \frac{18(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(ln(x + 1) - x)^{3}} - 12(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})x - \frac{12}{(ln(x + 1) - x)^{4}} - \frac{18(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})}{(x + 1)^{2}} - \frac{18(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(ln(x + 1) - x)^{4}} + \frac{6(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})}{(x + 1)^{3}} + \frac{6(\frac{-3(1 + 0)}{(x + 1)^{4}})}{(ln(x + 1) - x)^{4}} + \frac{6(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}})}{(x + 1)^{3}} + \frac{6(\frac{-3(1 + 0)}{(x + 1)^{4}})}{(ln(x + 1) - x)^{3}} + \frac{18(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})}{(x + 1)} + \frac{18(\frac{-(1 + 0)}{(x + 1)^{2}})}{(ln(x + 1) - x)^{4}} + \frac{2(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}})}{(x + 1)^{3}} + \frac{2(\frac{-3(1 + 0)}{(x + 1)^{4}})}{(ln(x + 1) - x)^{2}} - 12(\frac{-3(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{4}}) - 6(\frac{-2(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{3}}) - 6(\frac{-4(\frac{(1 + 0)}{(x + 1)} - 1)}{(ln(x + 1) - x)^{5}})\\=&\frac{24xe^{2}}{(ln(x + 1) - x)^{5}(x + 1)^{4}} - \frac{96xe^{2}}{(ln(x + 1) - x)^{5}(x + 1)^{3}} + \frac{30xe^{2}}{(x + 1)^{4}(ln(x + 1) - x)^{4}} - \frac{24e^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} + \frac{144xe^{2}}{(ln(x + 1) - x)^{5}(x + 1)^{2}} - \frac{60xe^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} + \frac{72e^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{16xe^{2}}{(x + 1)^{4}(ln(x + 1) - x)^{3}} - \frac{12xe^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{4}} - \frac{4e^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{3}} - \frac{20e^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{3}} - \frac{96xe^{2}}{(ln(x + 1) - x)^{5}(x + 1)} + \frac{30xe^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} - \frac{72e^{2}}{(ln(x + 1) - x)^{4}(x + 1)} - \frac{8xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{20e^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{6xe^{2}}{(x + 1)^{4}(ln(x + 1) - x)^{2}} - \frac{8xe^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{3}} - \frac{4e^{2}}{(x + 1)^{3}(ln(x + 1) - x)^{2}} + \frac{6xe^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{4}} + \frac{6xe^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{4}} + \frac{6xe^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{4}} + \frac{4e^{2}}{(x + 1)^{2}(ln(x + 1) - x)^{3}} - \frac{4e^{2}}{(ln(x + 1) - x)^{2}(x + 1)^{3}} + \frac{24xe^{2}}{(ln(x + 1) - x)^{5}} + \frac{24e^{2}}{(ln(x + 1) - x)^{4}} - \frac{24x^{2}}{(ln(x + 1) - x)^{5}(x + 1)^{4}} + \frac{96x^{2}}{(ln(x + 1) - x)^{5}(x + 1)^{3}} - \frac{36x^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{4}} + \frac{12x}{(x + 1)^{3}(ln(x + 1) - x)^{4}} - \frac{144x^{2}}{(ln(x + 1) - x)^{5}(x + 1)^{2}} + \frac{72x^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{3}} - \frac{48x}{(x + 1)^{2}(ln(x + 1) - x)^{4}} - \frac{22x^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{4}} + \frac{20x}{(x + 1)^{3}(ln(x + 1) - x)^{3}} + \frac{180x}{(ln(x + 1) - x)^{4}(x + 1)^{3}} + \frac{36x}{(x + 1)(ln(x + 1) - x)^{4}} + \frac{96x^{2}}{(ln(x + 1) - x)^{5}(x + 1)} - \frac{36x^{2}}{(ln(x + 1) - x)^{4}(x + 1)^{2}} - \frac{28x}{(x + 1)^{2}(ln(x + 1) - x)^{3}} + \frac{16x^{2}}{(ln(x + 1) - x)^{3}(x + 1)^{3}} + \frac{12x}{(x + 1)^{3}(ln(x + 1) - x)^{2}} - \frac{168x}{(ln(x + 1) - x)^{4}(x + 1)^{2}} + \frac{108x}{(ln(x + 1) - x)^{4}(x + 1)} - \frac{6x^{2}}{(ln(x + 1) - x)^{2}(x + 1)^{4}} + \frac{60x}{(ln(x + 1) - x)^{3}(x + 1)^{3}} - \frac{20x}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{4x}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{48x}{(ln(x + 1) - x)^{4}} - \frac{48x}{(ln(x + 1) - x)^{5}(x + 1)^{4}} + \frac{192x}{(ln(x + 1) - x)^{5}(x + 1)^{3}} - \frac{72x}{(ln(x + 1) - x)^{4}(x + 1)^{4}} - \frac{288x}{(ln(x + 1) - x)^{5}(x + 1)^{2}} - \frac{24x^{2}}{(ln(x + 1) - x)^{5}} - \frac{44x}{(ln(x + 1) - x)^{3}(x + 1)^{4}} + \frac{192x}{(ln(x + 1) - x)^{5}(x + 1)} - \frac{12x}{(ln(x + 1) - x)^{2}(x + 1)^{4}} + \frac{64}{(ln(x + 1) - x)^{3}(x + 1)^{3}} - \frac{180}{(ln(x + 1) - x)^{4}(x + 1)^{2}} - \frac{68}{(ln(x + 1) - x)^{3}(x + 1)^{2}} + \frac{40}{(ln(x + 1) - x)^{3}(x + 1)} - \frac{4}{(x + 1)^{2}(ln(x + 1) - x)^{3}} - \frac{6}{(ln(x + 1) - x)^{2}(x + 1)^{2}} + \frac{144}{(ln(x + 1) - x)^{4}(x + 1)} - \frac{6}{(x + 1)^{2}(ln(x + 1) - x)^{2}} + \frac{120}{(ln(x + 1) - x)^{4}(x + 1)^{3}} + \frac{8}{(x + 1)(ln(x + 1) - x)^{3}} + \frac{16}{(ln(x + 1) - x)^{2}(x + 1)^{3}} - \frac{24}{(ln(x + 1) - x)^{5}(x + 1)^{4}} + \frac{96}{(ln(x + 1) - x)^{5}(x + 1)^{3}} - \frac{36}{(ln(x + 1) - x)^{4}(x + 1)^{4}} - \frac{48x}{(ln(x + 1) - x)^{5}} - \frac{144}{(ln(x + 1) - x)^{5}(x + 1)^{2}} - \frac{22}{(ln(x + 1) - x)^{3}(x + 1)^{4}} + \frac{96}{(ln(x + 1) - x)^{5}(x + 1)} - \frac{6}{(ln(x + 1) - x)^{2}(x + 1)^{4}} - \frac{24}{(ln(x + 1) - x)^{3}} - \frac{48}{(ln(x + 1) - x)^{4}} - \frac{24}{(ln(x + 1) - x)^{5}}\\ \end{split}\end{equation} \]