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

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