There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2} + 1 - {({x}^{3} + 1)}^{(\frac{2}{3})})}{(2x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x + \frac{\frac{1}{2}}{x} - \frac{\frac{1}{2}(x^{3} + 1)^{\frac{2}{3}}}{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x + \frac{\frac{1}{2}}{x} - \frac{\frac{1}{2}(x^{3} + 1)^{\frac{2}{3}}}{x}\right)}{dx}\\=&\frac{1}{2} + \frac{\frac{1}{2}*-1}{x^{2}} - \frac{\frac{1}{2}(\frac{\frac{2}{3}(3x^{2} + 0)}{(x^{3} + 1)^{\frac{1}{3}}})}{x} - \frac{\frac{1}{2}(x^{3} + 1)^{\frac{2}{3}}*-1}{x^{2}}\\=& - \frac{1}{2x^{2}} - \frac{x}{(x^{3} + 1)^{\frac{1}{3}}} + \frac{(x^{3} + 1)^{\frac{2}{3}}}{2x^{2}} + \frac{1}{2}\\ \end{split}\end{equation} \]

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