There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ x{2}^{(\frac{-1}{x})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x{2}^{(\frac{-1}{x})}\right)}{dx}\\=&{2}^{(\frac{-1}{x})} + x({2}^{(\frac{-1}{x})}((\frac{--1}{x^{2}})ln(2) + \frac{(\frac{-1}{x})(0)}{(2)}))\\=&{2}^{(\frac{-1}{x})} + \frac{{2}^{(\frac{-1}{x})}ln(2)}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {2}^{(\frac{-1}{x})} + \frac{{2}^{(\frac{-1}{x})}ln(2)}{x}\right)}{dx}\\=&({2}^{(\frac{-1}{x})}((\frac{--1}{x^{2}})ln(2) + \frac{(\frac{-1}{x})(0)}{(2)})) + \frac{-{2}^{(\frac{-1}{x})}ln(2)}{x^{2}} + \frac{({2}^{(\frac{-1}{x})}((\frac{--1}{x^{2}})ln(2) + \frac{(\frac{-1}{x})(0)}{(2)}))ln(2)}{x} + \frac{{2}^{(\frac{-1}{x})}*0}{x(2)}\\=&\frac{{2}^{(\frac{-1}{x})}ln^{2}(2)}{x^{3}}\\ \end{split}\end{equation} \]

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