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

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