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

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