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

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