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

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