There are 1 questions in this calculation: for each question, the 6 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 6th\ derivative\ of\ function\ {x}^{\frac{1}{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 6th\ derivative\ of\ function:} \\=&\frac{720{x}^{\frac{1}{x}}ln(x)}{x^{7}} + \frac{1800{x}^{\frac{1}{x}}ln^{2}(x)}{x^{8}} + \frac{1200{x}^{\frac{1}{x}}ln^{3}(x)}{x^{9}} - \frac{6264{x}^{\frac{1}{x}}ln(x)}{x^{8}} + \frac{300{x}^{\frac{1}{x}}ln^{4}(x)}{x^{10}} - \frac{5130{x}^{\frac{1}{x}}ln^{2}(x)}{x^{9}} + \frac{30{x}^{\frac{1}{x}}ln^{5}(x)}{x^{11}} - \frac{1480{x}^{\frac{1}{x}}ln^{3}(x)}{x^{10}} + \frac{{x}^{\frac{1}{x}}ln^{6}(x)}{x^{12}} - \frac{165{x}^{\frac{1}{x}}ln^{4}(x)}{x^{11}} + \frac{7050{x}^{\frac{1}{x}}ln(x)}{x^{9}} - \frac{6{x}^{\frac{1}{x}}ln^{5}(x)}{x^{12}} + \frac{15{x}^{\frac{1}{x}}ln^{4}(x)}{x^{12}} + \frac{2685{x}^{\frac{1}{x}}ln^{2}(x)}{x^{10}} + \frac{360{x}^{\frac{1}{x}}ln^{3}(x)}{x^{11}} - \frac{20{x}^{\frac{1}{x}}ln^{3}(x)}{x^{12}} - \frac{390{x}^{\frac{1}{x}}ln^{2}(x)}{x^{11}} + \frac{15{x}^{\frac{1}{x}}ln^{2}(x)}{x^{12}} - \frac{2130{x}^{\frac{1}{x}}ln(x)}{x^{10}} + \frac{210{x}^{\frac{1}{x}}ln(x)}{x^{11}} - \frac{6{x}^{\frac{1}{x}}ln(x)}{x^{12}} - \frac{1764{x}^{\frac{1}{x}}}{x^{7}} + \frac{5104{x}^{\frac{1}{x}}}{x^{8}} + \frac{625{x}^{\frac{1}{x}}}{x^{10}} - \frac{3135{x}^{\frac{1}{x}}}{x^{9}} - \frac{45{x}^{\frac{1}{x}}}{x^{11}} + \frac{{x}^{\frac{1}{x}}}{x^{12}}\\ \end{split}\end{equation} \]

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