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

Your problem has not been solved here? Please take a look at the  hot problems ！