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

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