There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(x{(x + {x}^{\frac{1}{2}})}^{\frac{1}{2}})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x + x^{\frac{1}{2}})^{\frac{1}{4}}x^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x + x^{\frac{1}{2}})^{\frac{1}{4}}x^{\frac{1}{2}}\right)}{dx}\\=&(\frac{\frac{1}{4}(1 + \frac{\frac{1}{2}}{x^{\frac{1}{2}}})}{(x + x^{\frac{1}{2}})^{\frac{3}{4}}})x^{\frac{1}{2}} + \frac{(x + x^{\frac{1}{2}})^{\frac{1}{4}}*\frac{1}{2}}{x^{\frac{1}{2}}}\\=&\frac{x^{\frac{1}{2}}}{4(x + x^{\frac{1}{2}})^{\frac{3}{4}}} + \frac{(x + x^{\frac{1}{2}})^{\frac{1}{4}}}{2x^{\frac{1}{2}}} + \frac{1}{8(x + x^{\frac{1}{2}})^{\frac{3}{4}}}\\ \end{split}\end{equation} \]

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