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

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