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

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