There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{4} - {x}^{2})}{({x}^{6} + 2{x}^{3} - 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{4}}{(x^{6} + 2x^{3} - 1)} - \frac{x^{2}}{(x^{6} + 2x^{3} - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{4}}{(x^{6} + 2x^{3} - 1)} - \frac{x^{2}}{(x^{6} + 2x^{3} - 1)}\right)}{dx}\\=&(\frac{-(6x^{5} + 2*3x^{2} + 0)}{(x^{6} + 2x^{3} - 1)^{2}})x^{4} + \frac{4x^{3}}{(x^{6} + 2x^{3} - 1)} - (\frac{-(6x^{5} + 2*3x^{2} + 0)}{(x^{6} + 2x^{3} - 1)^{2}})x^{2} - \frac{2x}{(x^{6} + 2x^{3} - 1)}\\=&\frac{-6x^{9}}{(x^{6} + 2x^{3} - 1)^{2}} - \frac{6x^{6}}{(x^{6} + 2x^{3} - 1)^{2}} + \frac{4x^{3}}{(x^{6} + 2x^{3} - 1)} + \frac{6x^{7}}{(x^{6} + 2x^{3} - 1)^{2}} + \frac{6x^{4}}{(x^{6} + 2x^{3} - 1)^{2}} - \frac{2x}{(x^{6} + 2x^{3} - 1)}\\ \end{split}\end{equation} \]

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