There are 1 questions in this calculation: for each question, the 5 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 5th\ derivative\ of\ function\ log_{log_{2}^{x}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 5th\ derivative\ of\ function:} \\=&\frac{24}{x^{5}ln(log_{2}^{x})} + \frac{50}{x^{5}log(2, x)ln(2)ln^{2}(log_{2}^{x})} + \frac{70}{x^{5}{\left(log(2, x)^{2}ln^{2}(2)ln^{2}(log_{2}^{x})} + \frac{140}{x^{5}{\left(log(2, x)^{2}ln^{2}(2)ln^{3}(log_{2}^{x})} + \frac{60}{x^{5}{\left(log(2, x)^{3}ln^{3}(2)ln^{2}(log_{2}^{x})} + \frac{180}{x^{5}{\left(log(2, x)^{3}ln^{3}(2)ln^{3}(log_{2}^{x})} + \frac{180}{x^{5}{\left(log(2, x)^{3}ln^{3}(2)ln^{4}(log_{2}^{x})} + \frac{24}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{2}(log_{2}^{x})} + \frac{88}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{3}(log_{2}^{x})} + \frac{144}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{4}(log_{2}^{x})} + \frac{96}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{5}(log_{2}^{x})} - \frac{24log_{log_{2}^{x}}^{x}}{x^{5}log(2, x)ln(2)ln(log_{2}^{x})} - \frac{50log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{2}ln^{2}(2)ln(log_{2}^{x})} + \frac{50}{x^{5}log(2, x)ln^{2}(log_{2}^{x})ln(2)} - \frac{50log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{2}ln^{2}(2)ln^{2}(log_{2}^{x})} - \frac{50log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{2}ln^{2}(2)ln^{2}(log_{2}^{x})} - \frac{70log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{3}ln^{3}(2)ln(log_{2}^{x})} + \frac{35}{x^{5}{\left(log(2, x)^{2}ln^{2}(log_{2}^{x})ln^{2}(2)} - \frac{35log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{3}ln^{3}(2)ln^{2}(log_{2}^{x})} - \frac{175log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{3}ln^{3}(2)ln^{2}(log_{2}^{x})} + \frac{70}{x^{5}{\left(log(2, x)^{2}ln^{3}(log_{2}^{x})ln^{2}(2)} - \frac{70log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{3}ln^{3}(2)ln^{3}(log_{2}^{x})} - \frac{140log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{3}ln^{3}(2)ln^{3}(log_{2}^{x})} - \frac{60log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln(log_{2}^{x})} + \frac{20}{x^{5}{\left(log(2, x)^{3}ln^{2}(log_{2}^{x})ln^{3}(2)} - \frac{20log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{2}(log_{2}^{x})} - \frac{200log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{2}(log_{2}^{x})} + \frac{60}{x^{5}{\left(log(2, x)^{3}ln^{3}(log_{2}^{x})ln^{3}(2)} - \frac{60log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{3}(log_{2}^{x})} - \frac{300log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{3}(log_{2}^{x})} + \frac{60}{x^{5}{\left(log(2, x)^{3}ln^{4}(log_{2}^{x})ln^{3}(2)} - \frac{60log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{4}(log_{2}^{x})} - \frac{180log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{4}(2)ln^{4}(log_{2}^{x})} - \frac{24log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{5}(2)ln(log_{2}^{x})} + \frac{6}{x^{5}{\left(log(2, x)^{4}ln^{2}(log_{2}^{x})ln^{4}(2)} - \frac{6log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{5}(2)ln^{2}(log_{2}^{x})} - \frac{94log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{5}(2)ln^{2}(log_{2}^{x})} + \frac{22}{x^{5}{\left(log(2, x)^{4}ln^{3}(log_{2}^{x})ln^{4}(2)} - \frac{22log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{5}(2)ln^{3}(log_{2}^{x})} - \frac{188log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{5}(2)ln^{3}(log_{2}^{x})} + \frac{36}{x^{5}{\left(log(2, x)^{4}ln^{4}(log_{2}^{x})ln^{4}(2)} - \frac{36log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{5}(2)ln^{4}(log_{2}^{x})} - \frac{204log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{5}(2)ln^{4}(log_{2}^{x})} + \frac{24}{x^{5}{\left(log(2, x)^{4}ln^{5}(log_{2}^{x})ln^{4}(2)} - \frac{24log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{5}(2)ln^{5}(log_{2}^{x})} - \frac{96log_{log_{2}^{x}}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{5}(2)ln^{5}(log_{2}^{x})}\\ \end{split}\end{equation} \]

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