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

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