There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(x + sqrt(1 + {x}^{2}))}^{\frac{1}{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x + sqrt(x^{2} + 1))^{\frac{1}{x}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x + sqrt(x^{2} + 1))^{\frac{1}{x}}\right)}{dx}\\=&((x + sqrt(x^{2} + 1))^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(x + sqrt(x^{2} + 1)) + \frac{(\frac{1}{x})(1 + \frac{(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}})}{(x + sqrt(x^{2} + 1))}))\\=&\frac{-(x + sqrt(x^{2} + 1))^{\frac{1}{x}}ln(x + sqrt(x^{2} + 1))}{x^{2}} + \frac{(x + sqrt(x^{2} + 1))^{\frac{1}{x}}}{(x^{2} + 1)^{\frac{1}{2}}(x + sqrt(x^{2} + 1))} + \frac{(x + sqrt(x^{2} + 1))^{\frac{1}{x}}}{(x + sqrt(x^{2} + 1))x}\\ \end{split}\end{equation} \]

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