There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{3}(2x + 1) - \frac{{x}^{2}(2{x}^{2} - 1)(2x - 1)}{(2{x}^{2} - 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2x^{4} + x^{3} - \frac{4x^{5}}{(2x^{2} - 1)} + \frac{2x^{4}}{(2x^{2} - 1)} + \frac{2x^{3}}{(2x^{2} - 1)} - \frac{x^{2}}{(2x^{2} - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2x^{4} + x^{3} - \frac{4x^{5}}{(2x^{2} - 1)} + \frac{2x^{4}}{(2x^{2} - 1)} + \frac{2x^{3}}{(2x^{2} - 1)} - \frac{x^{2}}{(2x^{2} - 1)}\right)}{dx}\\=&2*4x^{3} + 3x^{2} - 4(\frac{-(2*2x + 0)}{(2x^{2} - 1)^{2}})x^{5} - \frac{4*5x^{4}}{(2x^{2} - 1)} + 2(\frac{-(2*2x + 0)}{(2x^{2} - 1)^{2}})x^{4} + \frac{2*4x^{3}}{(2x^{2} - 1)} + 2(\frac{-(2*2x + 0)}{(2x^{2} - 1)^{2}})x^{3} + \frac{2*3x^{2}}{(2x^{2} - 1)} - (\frac{-(2*2x + 0)}{(2x^{2} - 1)^{2}})x^{2} - \frac{2x}{(2x^{2} - 1)}\\=&8x^{3} + 3x^{2} + \frac{16x^{6}}{(2x^{2} - 1)^{2}} - \frac{20x^{4}}{(2x^{2} - 1)} - \frac{8x^{5}}{(2x^{2} - 1)^{2}} + \frac{8x^{3}}{(2x^{2} - 1)} - \frac{8x^{4}}{(2x^{2} - 1)^{2}} + \frac{6x^{2}}{(2x^{2} - 1)} + \frac{4x^{3}}{(2x^{2} - 1)^{2}} - \frac{2x}{(2x^{2} - 1)}\\ \end{split}\end{equation} \]

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