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

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