There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(\frac{(2{x}^{2} + 1)}{(sqrt({x}^{2} + 1))})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{2x^{2}}{sqrt(x^{2} + 1)} + \frac{1}{sqrt(x^{2} + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{2x^{2}}{sqrt(x^{2} + 1)} + \frac{1}{sqrt(x^{2} + 1)})\right)}{dx}\\=&\frac{(\frac{2*2x}{sqrt(x^{2} + 1)} + \frac{2x^{2}*-(2x + 0)*\frac{1}{2}}{(x^{2} + 1)(x^{2} + 1)^{\frac{1}{2}}} + \frac{-(2x + 0)*\frac{1}{2}}{(x^{2} + 1)(x^{2} + 1)^{\frac{1}{2}}})}{(\frac{2x^{2}}{sqrt(x^{2} + 1)} + \frac{1}{sqrt(x^{2} + 1)})}\\=&\frac{4x}{(\frac{2x^{2}}{sqrt(x^{2} + 1)} + \frac{1}{sqrt(x^{2} + 1)})sqrt(x^{2} + 1)} - \frac{2x^{3}}{(x^{2} + 1)^{\frac{3}{2}}(\frac{2x^{2}}{sqrt(x^{2} + 1)} + \frac{1}{sqrt(x^{2} + 1)})} - \frac{x}{(x^{2} + 1)^{\frac{3}{2}}(\frac{2x^{2}}{sqrt(x^{2} + 1)} + \frac{1}{sqrt(x^{2} + 1)})}\\ \end{split}\end{equation} \]

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