There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2} + 1 - \frac{{({x}^{3} + 1)}^{2}}{3})}{(2x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x + \frac{\frac{1}{3}}{x} - \frac{1}{6}x^{5} - \frac{1}{3}x^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x + \frac{\frac{1}{3}}{x} - \frac{1}{6}x^{5} - \frac{1}{3}x^{2}\right)}{dx}\\=&\frac{1}{2} + \frac{\frac{1}{3}*-1}{x^{2}} - \frac{1}{6}*5x^{4} - \frac{1}{3}*2x\\=& - \frac{1}{3x^{2}} - \frac{5x^{4}}{6} - \frac{2x}{3} + \frac{1}{2}\\ \end{split}\end{equation} \]

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