There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(x + {x}^{\frac{1}{2}})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x + {x}^{\frac{1}{2}})^{\frac{1}{2}}\right)}{dx}\\=&((x + {x}^{\frac{1}{2}})^{\frac{1}{2}}((0)ln(x + {x}^{\frac{1}{2}}) + \frac{(\frac{1}{2})(1 + ({x}^{\frac{1}{2}}((0)ln(x) + \frac{(\frac{1}{2})(1)}{(x)})))}{(x + {x}^{\frac{1}{2}})}))\\=&\frac{(x + x^{\frac{1}{2}})^{\frac{1}{2}}}{4(x + x^{\frac{1}{2}})x^{\frac{1}{2}}} + \frac{(x + x^{\frac{1}{2}})^{\frac{1}{2}}}{2(x + x^{\frac{1}{2}})}\\ \end{split}\end{equation} \]

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