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

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