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

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