There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(1 + {\frac{1}{x}}^{\frac{1}{2}})}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{1}{x^{\frac{1}{2}}} + 1)^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (\frac{1}{x^{\frac{1}{2}}} + 1)^{x}\right)}{dx}\\=&((\frac{1}{x^{\frac{1}{2}}} + 1)^{x}((1)ln(\frac{1}{x^{\frac{1}{2}}} + 1) + \frac{(x)(\frac{\frac{-1}{2}}{x^{\frac{3}{2}}} + 0)}{(\frac{1}{x^{\frac{1}{2}}} + 1)}))\\=&(\frac{1}{x^{\frac{1}{2}}} + 1)^{x}ln(\frac{1}{x^{\frac{1}{2}}} + 1) - \frac{(\frac{1}{x^{\frac{1}{2}}} + 1)^{x}}{2(\frac{1}{x^{\frac{1}{2}}} + 1)x^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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