There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {x}^{\frac{1}{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {x}^{\frac{1}{x}}\right)}{dx}\\=&({x}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x) + \frac{(\frac{1}{x})(1)}{(x)}))\\=&\frac{-{x}^{\frac{1}{x}}ln(x)}{x^{2}} + \frac{{x}^{\frac{1}{x}}}{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-{x}^{\frac{1}{x}}ln(x)}{x^{2}} + \frac{{x}^{\frac{1}{x}}}{x^{2}}\right)}{dx}\\=&\frac{--2{x}^{\frac{1}{x}}ln(x)}{x^{3}} - \frac{({x}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x) + \frac{(\frac{1}{x})(1)}{(x)}))ln(x)}{x^{2}} - \frac{{x}^{\frac{1}{x}}}{x^{2}(x)} + \frac{-2{x}^{\frac{1}{x}}}{x^{3}} + \frac{({x}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x) + \frac{(\frac{1}{x})(1)}{(x)}))}{x^{2}}\\=&\frac{2{x}^{\frac{1}{x}}ln(x)}{x^{3}} + \frac{{x}^{\frac{1}{x}}ln^{2}(x)}{x^{4}} - \frac{2{x}^{\frac{1}{x}}ln(x)}{x^{4}} - \frac{3{x}^{\frac{1}{x}}}{x^{3}} + \frac{{x}^{\frac{1}{x}}}{x^{4}}\\ \end{split}\end{equation} \]

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