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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {x}^{\frac{1}{(x - \frac{1}{x})}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {x}^{\frac{1}{(x - \frac{1}{x})}}\right)}{dx}\\=&({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))\\=&\frac{-{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{2}} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{2}} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x}\right)}{dx}\\=&\frac{-(\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{2}} - \frac{-2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{3}} - \frac{({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{2}x^{2}} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{2}(x)} - (\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x) - \frac{({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{2}} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}(x)} + \frac{(\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x} + \frac{-{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x^{2}} + \frac{({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})x}\\=&\frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{4}} + \frac{4{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{2}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{3}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{4}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{2}} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{3}} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{3}} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x^{2}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{4}} + \frac{4{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{2}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{3}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{4}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{2}} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{3}} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{3}} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x^{2}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{2}}\right)}{dx}\\=&\frac{2(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{4}} + \frac{2*-4{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{5}} + \frac{2({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{3}x^{4}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{4}(x)} + \frac{4(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{2}} + \frac{4*-2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{3}} + \frac{4({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{3}x^{2}} + \frac{4{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{2}(x)} + \frac{2(\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{3}} + \frac{2*-3{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{4}} + \frac{2({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{2}x^{3}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{3}(x)} + \frac{(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x^{4}} + \frac{-4{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{5}} + \frac{({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{4}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{4}x^{4}(x)} + \frac{2(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x^{2}} + \frac{2*-2{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{3}} + \frac{2({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{2}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{4}x^{2}(x)} - \frac{2(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{3}} - \frac{2*-3{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{4}} - \frac{2({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{3}x^{3}} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{3}(x)} - \frac{2(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x} - \frac{2*-{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{2}} - \frac{2({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{3}x} - \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x(x)} + 2(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x) + \frac{2({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{3}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}(x)} + (\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x) + \frac{({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{4}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{4}(x)} - \frac{2(\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{3}} - \frac{2*-3{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{4}} - \frac{2({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{2}x^{3}} - \frac{2(\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x} - \frac{2*-{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{2}} - \frac{2({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{2}x} - \frac{(\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{2}} - \frac{-2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x^{3}} - \frac{({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})x^{2}} + \frac{(\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{2}} + \frac{-2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{3}} + \frac{({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{2}x^{2}}\\=&\frac{-6{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{6}} - \frac{21{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{4}} - \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{5}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{6}} - \frac{18{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{4}} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{5}} - \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{3}} - \frac{21{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{2}} + \frac{9{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{4}} - \frac{18{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{2}} + \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{3}} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{2}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{4}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{5}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{3}} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{6}} - \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{4}} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{5}} - \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{2}} + \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{3}} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{4}} + \frac{9{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{4}} + \frac{13{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{3}} + \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{5}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{2}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}} + \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{2}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x^{3}} - \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{6}} - \frac{21{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{4}} - \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{5}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{6}} - \frac{18{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{4}} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{5}} - \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{3}} - \frac{21{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{2}} + \frac{9{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{4}} - \frac{18{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{2}} + \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{3}} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{2}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{4}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{5}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{3}} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{6}} - \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{4}} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{5}} - \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{2}} + \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{3}} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{4}} + \frac{9{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{4}} + \frac{13{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{3}} + \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{5}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{2}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}} + \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{2}} + \frac{2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x^{3}} - \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{3}}\right)}{dx}\\=&\frac{-6(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{6}} - \frac{6*-6{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{7}} - \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{4}x^{6}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{6}(x)} - \frac{21(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{4}} - \frac{21*-4{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{5}} - \frac{21({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{4}x^{4}} - \frac{21{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{4}(x)} - \frac{12(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{5}} - \frac{12*-5{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{6}} - \frac{12({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{3}x^{5}} - \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{5}(x)} - \frac{6(\frac{-5(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{6}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x^{6}} - \frac{6*-6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{7}} - \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{6}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{5}x^{6}(x)} - \frac{18(\frac{-5(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{6}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x^{4}} - \frac{18*-4{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{5}} - \frac{18({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{4}} - \frac{18{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{5}x^{4}(x)} + \frac{12(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{5}} + \frac{12*-5{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{6}} + \frac{12({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{4}x^{5}} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{5}(x)} - \frac{12(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{3}} - \frac{12*-3{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{4}} - \frac{12({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{3}x^{3}} - \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{3}(x)} - \frac{21(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{2}} - \frac{21*-2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{3}} - \frac{21({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{4}x^{2}} - \frac{21{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{2}(x)} + \frac{9(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{4}} + \frac{9*-4{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{5}} + \frac{9({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{3}x^{4}} + \frac{9{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{4}(x)} - \frac{18(\frac{-5(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{6}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x^{2}} - \frac{18*-2{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{3}} - \frac{18({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{2}} - \frac{18{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{5}x^{2}(x)} + \frac{24(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{3}} + \frac{24*-3{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{4}} + \frac{24({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{4}x^{3}} + \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{3}(x)} + \frac{3(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{2}} + \frac{3*-2{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{3}} + \frac{3({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{3}x^{2}} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{2}(x)} - \frac{6(\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x^{4}} - \frac{6*-4{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{5}} - \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{2}x^{4}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{4}(x)} - \frac{6(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x^{5}} - \frac{6*-5{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{6}} - \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{5}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{4}x^{5}(x)} - \frac{6(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x^{3}} - \frac{6*-3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{4}} - \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{3}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{4}x^{3}(x)} - \frac{(\frac{-6(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{7}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{x^{6}} - \frac{-6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{7}} - \frac{({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{6}} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}*3ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{6}(x)} - \frac{3(\frac{-6(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{7}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{x^{4}} - \frac{3*-4{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{5}} - \frac{3({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{4}} - \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}*3ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{4}(x)} + \frac{3(\frac{-5(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{6}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x^{5}} + \frac{3*-5{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{6}} + \frac{3({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{5}} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{5}x^{5}(x)} - \frac{3(\frac{-6(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{7}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{x^{2}} - \frac{3*-2{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{3}} - \frac{3({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{2}} - \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}*3ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{2}(x)} + \frac{6(\frac{-5(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{6}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x^{3}} + \frac{6*-3{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{4}} + \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{3}} + \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{5}x^{3}(x)} + \frac{12(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{x} + \frac{12*-{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{2}} + \frac{12({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{4}x} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x(x)} + \frac{3(\frac{-5(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{6}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{x} + \frac{3*-{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{2}} + \frac{3({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{5}x} + \frac{3{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{5}x(x)} - \frac{6(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{4}} - \frac{6*-4{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{5}} - \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{3}x^{4}} + \frac{9(\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{4}} + \frac{9*-4{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{5}} + \frac{9({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{2}x^{4}} + \frac{13(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{3}} + \frac{13*-3{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{4}} + \frac{13({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{3}x^{3}} + \frac{6(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{5}} + \frac{6*-5{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{6}} + \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{3}x^{5}} - \frac{6(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{2}} - \frac{6*-2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{3}} - \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{3}x^{2}} - 6(\frac{-4(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{5}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln(x) - \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln(x)}{(x - \frac{1}{x})^{4}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}(x)} - 6(\frac{-5(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{6}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x) - \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{2}(x)}{(x - \frac{1}{x})^{5}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}*2ln(x)}{(x - \frac{1}{x})^{5}(x)} + \frac{6(\frac{-3(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{4}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x} + \frac{6*-{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{2}} + \frac{6({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{3}x} - (\frac{-6(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{7}}){x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x) - \frac{({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))ln^{3}(x)}{(x - \frac{1}{x})^{6}} - \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}*3ln^{2}(x)}{(x - \frac{1}{x})^{6}(x)} + \frac{3(\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{2}} + \frac{3*-2{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{3}} + \frac{3({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{2}x^{2}} + \frac{2(\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{3}} + \frac{2*-3{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x^{4}} + \frac{2({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})x^{3}} - \frac{3(\frac{-2(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{3}}){x}^{\frac{1}{(x - \frac{1}{x})}}}{x^{3}} - \frac{3*-3{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{4}} - \frac{3({x}^{\frac{1}{(x - \frac{1}{x})}}(((\frac{-(1 - \frac{-1}{x^{2}})}{(x - \frac{1}{x})^{2}}))ln(x) + \frac{(\frac{1}{(x - \frac{1}{x})})(1)}{(x)}))}{(x - \frac{1}{x})^{2}x^{3}}\\=&\frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{5}x^{8}} + \frac{132{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{5}x^{6}} + \frac{72{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{7}} + \frac{36{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{8}} + \frac{150{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{6}} - \frac{72{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{5}x^{7}} + \frac{168{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{5}} + \frac{216{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{5}x^{4}} - \frac{120{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{6}} + \frac{228{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{4}} - \frac{220{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{5}x^{5}} + \frac{84{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{3}} + \frac{72{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{6}} + \frac{72{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{7}} + \frac{144{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{5}} + \frac{48{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{4}} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{7}x^{8}} + \frac{48{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{7}x^{6}} - \frac{36{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{7}} + \frac{72{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{7}x^{4}} - \frac{108{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{5}} - \frac{144{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{4}} + \frac{36{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{6}} - \frac{44{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{5}} + \frac{72{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{3}} - \frac{8{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{3}x^{3}} + \frac{132{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{5}x^{2}} + \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{4}x^{4}} + \frac{150{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{2}} - \frac{220{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{5}x^{3}} - \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{4}x^{2}} - \frac{30{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{6}} - \frac{36{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{4}} + \frac{48{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{7}x^{2}} - \frac{108{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{6}x^{3}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{5}x^{2}} + \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{2}x^{5}} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{7}} + \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{5}} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{6}x^{3}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{4}(x)}{(x - \frac{1}{x})^{8}x^{8}} + \frac{4{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{4}(x)}{(x - \frac{1}{x})^{8}x^{6}} - \frac{4{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{7}x^{7}} + \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{4}(x)}{(x - \frac{1}{x})^{8}x^{4}} - \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{7}x^{5}} + \frac{4{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{4}(x)}{(x - \frac{1}{x})^{8}x^{2}} - \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{7}x^{3}} - \frac{72{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{5}x} - \frac{36{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{6}x} - \frac{4{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{7}x} + \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{3}} + \frac{48{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{5}} - \frac{44{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{5}} + \frac{36{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{6}} - \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{7}} + \frac{73{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{4}} - \frac{84{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{5}} - \frac{84{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{3}} - \frac{78{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{4}} + \frac{36{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x^{2}} - \frac{60{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{6}} + \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}ln(x)}{(x - \frac{1}{x})^{5}} + \frac{36{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{2}(x)}{(x - \frac{1}{x})^{6}} - \frac{24{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{4}x} + \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{3}(x)}{(x - \frac{1}{x})^{7}} - \frac{12{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{3}x^{2}} + \frac{{x}^{\frac{1}{(x - \frac{1}{x})}}ln^{4}(x)}{(x - \frac{1}{x})^{8}} - \frac{8{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{3}} - \frac{6{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})x^{4}} + \frac{11{x}^{\frac{1}{(x - \frac{1}{x})}}}{(x - \frac{1}{x})^{2}x^{4}}\\ \end{split}\end{equation} \]