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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {{ln(x)}^{ln(x)}}^{ln(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{ln(x)}^{ln(x)}}^{ln(x)}\right)}{dx}\\=&({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))\\=&\frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x}\right)}{dx}\\=&\frac{-{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{2}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln(ln(x))}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x(ln(x))(x)} + \frac{-{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x({ln(x)}^{ln(x)})} + \frac{-{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{2}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}}{x(x)}\\=&\frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{2}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{2}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{2}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{2}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{2}}\right)}{dx}\\=&\frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)ln(ln(x))}{x^{2}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{2}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{2}(ln(x))(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{2}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{2}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{2}({ln(x)}^{ln(x)})} - \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{3}} - \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln(ln(x))}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{2}(x)} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{2}(ln(x))(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln(ln(x))}{x^{2}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{2}(ln(x))(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)}{x^{2}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln^{2}(x)}{x^{2}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))*2ln(x)}{x^{2}(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{2}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))*2ln(x)}{x^{2}(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{2}({ln(x)}^{ln(x)})} - \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{2}({ln(x)}^{ln(x)})} - \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}} - \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{2}(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{2}({ln(x)}^{ln(x)})} + \frac{2*-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))}{x^{2}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{2}(ln(x))(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)}{x^{2}(x)} + \frac{3*-2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}} + \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))}{x^{2}}\\=&\frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))}{x^{3}} + \frac{10{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}ln(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{3}} - \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))}{x^{3}} + \frac{10{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}ln(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{3}} - \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}}\right)}{dx}\\=&\frac{-3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}(ln(x))(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))*2ln(x)ln({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))ln(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(x)ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})*2ln(x)ln(ln(x))}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(ln(x))ln^{2}(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})*2ln(ln(x))ln^{2}(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))*2ln(x)}{x^{3}(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))*2ln(x)ln({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))ln^{2}(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))*2ln(x)}{x^{3}(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln(ln(x))}{x^{3}(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}(ln(x))(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln^{3}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln^{3}(x)}{x^{3}(ln(x))(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))*3ln^{2}(x)}{x^{3}(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)}{x^{3}({ln(x)}^{ln(x)})} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln^{2}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln^{2}(x)}{x^{3}(ln(x))(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))*2ln(x)}{x^{3}(x)} + \frac{7*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)}{x^{4}} + \frac{7({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln(x)}{x^{3}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}(ln(x))(x)} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}(x)} + \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{4*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)}{x^{4}} + \frac{4({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln(x)}{x^{3}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln(x)}{x^{3}(ln(x))(x)} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))}{x^{3}(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}(ln(x))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}(ln(x))ln^{3}(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))*3ln^{2}(x)}{x^{3}(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln^{2}(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)*2ln(ln(x))}{x^{3}(ln(x))(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln^{2}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}(ln(x))(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))*2ln(x)}{x^{3}(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}(x)ln(ln(x))}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}(x)ln^{2}(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}(x)ln^{2}(ln(x))}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)*2ln(ln(x))}{x^{3}(ln(x))(x)} + \frac{10*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{4}} + \frac{10({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln(ln(x))}{x^{3}} + \frac{10{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}(x)} + \frac{10{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})*2ln(x)}{x^{3}(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))*3ln^{2}(x)}{x^{3}(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{11*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{4}} + \frac{11({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}(x)} - \frac{6*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{4}} - \frac{6({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))}{x^{3}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}(ln(x))(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}ln(x)} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))}{x^{3}ln(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*-1}{x^{3}ln^{2}(x)(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)}{x^{3}(x)} + \frac{11*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{11({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}(x)}{x^{3}(x)} - \frac{9*-3{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}} - \frac{9({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))}{x^{3}}\\=&\frac{25{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{8{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{24{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{4}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{8{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})ln(x)}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln^{2}({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln({ln(x)}^{ln(x)})ln^{2}(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{3}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{3}(ln(x))ln^{3}(x)}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln^{2}(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{3}(x)ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{3}(x)ln^{2}(ln(x))}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{3}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{3}({ln(x)}^{ln(x)})}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)}{x^{4}} + \frac{29{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{4}} + \frac{17{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln^{2}(ln(x))}{x^{4}} + \frac{36{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{4}} - \frac{18{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)}{x^{4}} - \frac{42{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{2}(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{4}ln(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(ln(x))ln^{4}(x)}{x^{4}} - \frac{54{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{4}} - \frac{24{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)}{x^{4}} + \frac{30{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln^{3}(ln(x))}{x^{4}} + \frac{5{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{4}ln(x)} + \frac{28{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{4}(x)}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))}{x^{4}} + \frac{5{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{41{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{4}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{18{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(x)ln^{2}(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(x)ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln^{2}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{3}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(x)ln^{3}(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{4}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{4}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{3}({ln(x)}^{ln(x)})}{x^{4}} + \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))}{x^{4}} + \frac{66{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}ln(x)} - \frac{60{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{4}} - \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}ln^{2}(x)} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})}{x^{4}} + \frac{29{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{4}} - \frac{60{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}({ln(x)}^{ln(x)})}{x^{4}} + \frac{29{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(x)}{x^{4}} + \frac{68{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {{ln(x)}^{ln(x)}}^{ln(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{ln(x)}^{ln(x)}}^{ln(x)}\right)}{dx}\\=&({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))\\=&\frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x}\right)}{dx}\\=&\frac{-{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{2}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln(ln(x))}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x(ln(x))(x)} + \frac{-{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x({ln(x)}^{ln(x)})} + \frac{-{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{2}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)}{x} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}}{x(x)}\\=&\frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{2}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{2}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{2}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{2}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{2}}\right)}{dx}\\=&\frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)ln(ln(x))}{x^{2}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{2}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{2}(ln(x))(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{2}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{2}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{2}({ln(x)}^{ln(x)})} - \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{3}} - \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln(ln(x))}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{2}(x)} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{2}(ln(x))(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln(ln(x))}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln(ln(x))}{x^{2}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{2}(ln(x))(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)}{x^{2}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln^{2}(x)}{x^{2}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))*2ln(x)}{x^{2}(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{2}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))*2ln(x)}{x^{2}(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln({ln(x)}^{ln(x)})}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{2}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{2}({ln(x)}^{ln(x)})} - \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{2}({ln(x)}^{ln(x)})} - \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}} - \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)}{x^{2}} - \frac{{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{2}(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{2}({ln(x)}^{ln(x)})} + \frac{2*-2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))}{x^{2}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{2}(ln(x))(x)} + \frac{-2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)}{x^{2}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)}{x^{2}(x)} + \frac{3*-2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}} + \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))}{x^{2}}\\=&\frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))}{x^{3}} + \frac{10{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}ln(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{3}} - \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))}{x^{3}} + \frac{10{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}ln(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{3}} - \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}}\right)}{dx}\\=&\frac{-3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}(ln(x))(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))*2ln(x)ln({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))ln(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(x)ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})*2ln(x)ln(ln(x))}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(ln(x))ln^{2}(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})*2ln(ln(x))ln^{2}(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))*2ln(x)}{x^{3}(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))*2ln(x)ln({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))ln^{2}(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))*2ln(x)}{x^{3}(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln(ln(x))}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln(ln(x))}{x^{3}(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}(ln(x))(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln^{3}(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln^{3}(x)}{x^{3}(ln(x))(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))*3ln^{2}(x)}{x^{3}(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)}{x^{3}({ln(x)}^{ln(x)})} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln^{2}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln^{2}(x)}{x^{3}(ln(x))(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))*2ln(x)}{x^{3}(x)} + \frac{7*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)}{x^{4}} + \frac{7({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln(x)}{x^{3}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}(ln(x))(x)} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}(x)} + \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{4*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)}{x^{4}} + \frac{4({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(ln(x))ln(x)}{x^{3}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(ln(x))ln(x)}{x^{3}(ln(x))(x)} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))}{x^{3}(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}(ln(x))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}(ln(x))ln^{3}(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))*3ln^{2}(x)}{x^{3}(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln^{2}(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)*2ln(ln(x))}{x^{3}(ln(x))(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln^{2}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{3}(ln(x))(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))*2ln(x)}{x^{3}(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}(x)} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{3}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln(ln(x))}{x^{3}({ln(x)}^{ln(x)})} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{3}(ln(x))(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}(x)ln(ln(x))}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}(x)ln(ln(x))}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}(x)ln^{2}(ln(x))}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}(x)ln^{2}(ln(x))}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)*2ln(ln(x))}{x^{3}(ln(x))(x)} + \frac{10*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{4}} + \frac{10({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln(ln(x))}{x^{3}} + \frac{10{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{3}(x)} + \frac{10{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{3}(ln(x))(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))ln^{2}(x)}{x^{3}({ln(x)}^{ln(x)})} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})*2ln(x)}{x^{3}(x)} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)ln({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{3}(ln(x))(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))*3ln^{2}(x)}{x^{3}(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{3}(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{11*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{4}} + \frac{11({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(x)}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}(x)} - \frac{6*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{4}} - \frac{6({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln(ln(x))}{x^{3}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{3}(ln(x))(x)} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}({ln(x)}^{ln(x)})}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}*2ln({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{2*-3{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}ln(x)} + \frac{2({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))}{x^{3}ln(x)} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}*-1}{x^{3}ln^{2}(x)(x)} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}({ln(x)}^{ln(x)})}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}({ln(x)}^{ln(x)})({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} - \frac{3*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{4}} - \frac{3({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{2}(x)}{x^{3}} - \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}*2ln(x)}{x^{3}(x)} + \frac{11*-3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{11({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln({ln(x)}^{ln(x)})}{x^{3}} + \frac{11{{ln(x)}^{ln(x)}}^{ln(x)}({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))}))}{x^{3}({ln(x)}^{ln(x)})} + \frac{-3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{4}} + \frac{({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))ln^{3}(x)}{x^{3}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}*3ln^{2}(x)}{x^{3}(x)} - \frac{9*-3{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}} - \frac{9({{ln(x)}^{ln(x)}}^{ln(x)}((\frac{1}{(x)})ln({ln(x)}^{ln(x)}) + \frac{(ln(x))(({ln(x)}^{ln(x)}((\frac{1}{(x)})ln(ln(x)) + \frac{(ln(x))(\frac{1}{(x)})}{(ln(x))})))}{({ln(x)}^{ln(x)})}))}{x^{3}}\\=&\frac{25{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{8{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{24{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})ln(x)ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{4}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{8{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})ln(x)}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)ln(ln(x))}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln^{2}({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{2}(x)}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})ln(ln(x))ln(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln({ln(x)}^{ln(x)})ln^{2}(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))ln^{2}(x)}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln^{3}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{4{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(ln(x))ln(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{3}(ln(x))ln^{3}(x)}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)ln^{2}(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{3}(x)ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{3}(x)ln^{2}(ln(x))}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))ln^{3}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)ln^{3}({ln(x)}^{ln(x)})}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{3}(x)}{x^{4}} + \frac{29{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}(x)}{x^{4}} + \frac{17{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln^{2}(ln(x))}{x^{4}} + \frac{36{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{2}(x)}{x^{4}} - \frac{18{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{3}(x)}{x^{4}} - \frac{42{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln(x)}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}(ln(x))}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{9{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{2}(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{4}ln(x)} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(ln(x))ln^{4}(x)}{x^{4}} - \frac{54{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln(ln(x))}{x^{4}} - \frac{24{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln(x)}{x^{4}} + \frac{30{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln^{3}(ln(x))}{x^{4}} + \frac{5{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{4}ln(x)} + \frac{28{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))ln^{4}(x)}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln(ln(x))}{x^{4}} + \frac{5{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{41{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln^{2}(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{2}(x)}{x^{4}} + \frac{7{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{18{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{3}(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})ln(x)}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(x)ln^{2}(ln(x))}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{2}({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(x)ln(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})ln^{2}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})ln^{3}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(x)ln^{3}(ln(x))}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)ln({ln(x)}^{ln(x)})}{x^{4}} + \frac{3{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(ln(x))ln^{4}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))ln^{4}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)ln^{3}({ln(x)}^{ln(x)})}{x^{4}} + \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(ln(x))}{x^{4}} + \frac{66{{ln(x)}^{ln(x)}}^{ln(x)}ln(ln(x))}{x^{4}} - \frac{12{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}ln(x)} - \frac{60{{ln(x)}^{ln(x)}}^{ln(x)}ln(x)}{x^{4}} - \frac{2{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}ln^{2}(x)} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}({ln(x)}^{ln(x)})}{x^{4}} + \frac{29{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}({ln(x)}^{ln(x)})}{x^{4}} - \frac{60{{ln(x)}^{ln(x)}}^{ln(x)}ln({ln(x)}^{ln(x)})}{x^{4}} - \frac{6{{ln(x)}^{ln(x)}}^{ln(x)}ln^{3}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}({ln(x)}^{ln(x)})}{x^{4}} + \frac{29{{ln(x)}^{ln(x)}}^{ln(x)}ln^{2}(x)}{x^{4}} + \frac{{{ln(x)}^{ln(x)}}^{ln(x)}ln^{4}(x)}{x^{4}} + \frac{68{{ln(x)}^{ln(x)}}^{ln(x)}}{x^{4}}\\ \end{split}\end{equation} \]