There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (sqrt(({\frac{1}{x}}^{2}) - 1)(-2)ln(x) + 2arctan(sqrt(({\frac{1}{x}}^{2}) - 1)) - sqrt(({\frac{1}{x}}^{2}) - 1)ln(({\frac{1}{x}}^{2}) - 1))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -2ln(x)sqrt(\frac{1}{x^{2}} - 1) + 2arctan(sqrt(\frac{1}{x^{2}} - 1)) - ln(\frac{1}{x^{2}} - 1)sqrt(\frac{1}{x^{2}} - 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -2ln(x)sqrt(\frac{1}{x^{2}} - 1) + 2arctan(sqrt(\frac{1}{x^{2}} - 1)) - ln(\frac{1}{x^{2}} - 1)sqrt(\frac{1}{x^{2}} - 1)\right)}{dx}\\=&\frac{-2sqrt(\frac{1}{x^{2}} - 1)}{(x)} - \frac{2ln(x)(\frac{-2}{x^{3}} + 0)*\frac{1}{2}}{(\frac{1}{x^{2}} - 1)^{\frac{1}{2}}} + 2(\frac{(\frac{(\frac{-2}{x^{3}} + 0)*\frac{1}{2}}{(\frac{1}{x^{2}} - 1)^{\frac{1}{2}}})}{(1 + (sqrt(\frac{1}{x^{2}} - 1))^{2})}) - \frac{(\frac{-2}{x^{3}} + 0)sqrt(\frac{1}{x^{2}} - 1)}{(\frac{1}{x^{2}} - 1)} - \frac{ln(\frac{1}{x^{2}} - 1)(\frac{-2}{x^{3}} + 0)*\frac{1}{2}}{(\frac{1}{x^{2}} - 1)^{\frac{1}{2}}}\\=&\frac{-2sqrt(\frac{1}{x^{2}} - 1)}{x} + \frac{2ln(x)}{(\frac{1}{x^{2}} - 1)^{\frac{1}{2}}x^{3}} - \frac{2}{(\frac{1}{x^{2}} - 1)^{\frac{1}{2}}(sqrt(\frac{1}{x^{2}} - 1)^{2} + 1)x^{3}} + \frac{2sqrt(\frac{1}{x^{2}} - 1)}{(\frac{1}{x^{2}} - 1)x^{3}} + \frac{ln(\frac{1}{x^{2}} - 1)}{(\frac{1}{x^{2}} - 1)^{\frac{1}{2}}x^{3}}\\ \end{split}\end{equation} \]

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