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

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