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

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