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

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