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

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