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

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