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

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