There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ x - \frac{({x}^{3} - {x}^{2} - 1)}{(3{x}^{2} - 2x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x - \frac{x^{3}}{(3x^{2} - 2x)} + \frac{x^{2}}{(3x^{2} - 2x)} + \frac{1}{(3x^{2} - 2x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x - \frac{x^{3}}{(3x^{2} - 2x)} + \frac{x^{2}}{(3x^{2} - 2x)} + \frac{1}{(3x^{2} - 2x)}\right)}{dx}\\=&1 - (\frac{-(3*2x - 2)}{(3x^{2} - 2x)^{2}})x^{3} - \frac{3x^{2}}{(3x^{2} - 2x)} + (\frac{-(3*2x - 2)}{(3x^{2} - 2x)^{2}})x^{2} + \frac{2x}{(3x^{2} - 2x)} + (\frac{-(3*2x - 2)}{(3x^{2} - 2x)^{2}})\\=&\frac{6x^{4}}{(3x^{2} - 2x)^{2}} - \frac{8x^{3}}{(3x^{2} - 2x)^{2}} - \frac{3x^{2}}{(3x^{2} - 2x)} + \frac{2x^{2}}{(3x^{2} - 2x)^{2}} + \frac{2x}{(3x^{2} - 2x)} - \frac{6x}{(3x^{2} - 2x)^{2}} + \frac{2}{(3x^{2} - 2x)^{2}} + 1\\ \end{split}\end{equation} \]

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