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

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