There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {2}^{\frac{1}{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {2}^{\frac{1}{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}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-{2}^{\frac{1}{x}}ln(2)}{x^{2}}\right)}{dx}\\=&\frac{--2 * {2}^{\frac{1}{x}}ln(2)}{x^{3}} - \frac{({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln(2)}{x^{2}} - \frac{{2}^{\frac{1}{x}}*0}{x^{2}(2)}\\=&\frac{2 * {2}^{\frac{1}{x}}ln(2)}{x^{3}} + \frac{{2}^{\frac{1}{x}}ln^{2}(2)}{x^{4}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2 * {2}^{\frac{1}{x}}ln(2)}{x^{3}} + \frac{{2}^{\frac{1}{x}}ln^{2}(2)}{x^{4}}\right)}{dx}\\=&\frac{2*-3 * {2}^{\frac{1}{x}}ln(2)}{x^{4}} + \frac{2({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln(2)}{x^{3}} + \frac{2 * {2}^{\frac{1}{x}}*0}{x^{3}(2)} + \frac{-4 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{5}} + \frac{({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln^{2}(2)}{x^{4}} + \frac{{2}^{\frac{1}{x}}*2ln(2)*0}{x^{4}(2)}\\=&\frac{-6 * {2}^{\frac{1}{x}}ln(2)}{x^{4}} - \frac{6 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{5}} - \frac{{2}^{\frac{1}{x}}ln^{3}(2)}{x^{6}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6 * {2}^{\frac{1}{x}}ln(2)}{x^{4}} - \frac{6 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{5}} - \frac{{2}^{\frac{1}{x}}ln^{3}(2)}{x^{6}}\right)}{dx}\\=&\frac{-6*-4 * {2}^{\frac{1}{x}}ln(2)}{x^{5}} - \frac{6({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln(2)}{x^{4}} - \frac{6 * {2}^{\frac{1}{x}}*0}{x^{4}(2)} - \frac{6*-5 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{6}} - \frac{6({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln^{2}(2)}{x^{5}} - \frac{6 * {2}^{\frac{1}{x}}*2ln(2)*0}{x^{5}(2)} - \frac{-6 * {2}^{\frac{1}{x}}ln^{3}(2)}{x^{7}} - \frac{({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln^{3}(2)}{x^{6}} - \frac{{2}^{\frac{1}{x}}*3ln^{2}(2)*0}{x^{6}(2)}\\=&\frac{24 * {2}^{\frac{1}{x}}ln(2)}{x^{5}} + \frac{36 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{6}} + \frac{12 * {2}^{\frac{1}{x}}ln^{3}(2)}{x^{7}} + \frac{{2}^{\frac{1}{x}}ln^{4}(2)}{x^{8}}\\ \end{split}\end{equation} \]

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