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

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