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

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