There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-(4{x}^{3} - 9{x}^{2} + \frac{1}{2}x + 6)}{(4{x}^{2} - 6x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-4x^{3}}{(4x^{2} - 6x)} + \frac{9x^{2}}{(4x^{2} - 6x)} - \frac{\frac{1}{2}x}{(4x^{2} - 6x)} - \frac{6}{(4x^{2} - 6x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-4x^{3}}{(4x^{2} - 6x)} + \frac{9x^{2}}{(4x^{2} - 6x)} - \frac{\frac{1}{2}x}{(4x^{2} - 6x)} - \frac{6}{(4x^{2} - 6x)}\right)}{dx}\\=&-4(\frac{-(4*2x - 6)}{(4x^{2} - 6x)^{2}})x^{3} - \frac{4*3x^{2}}{(4x^{2} - 6x)} + 9(\frac{-(4*2x - 6)}{(4x^{2} - 6x)^{2}})x^{2} + \frac{9*2x}{(4x^{2} - 6x)} - \frac{1}{2}(\frac{-(4*2x - 6)}{(4x^{2} - 6x)^{2}})x - \frac{\frac{1}{2}}{(4x^{2} - 6x)} - 6(\frac{-(4*2x - 6)}{(4x^{2} - 6x)^{2}})\\=&\frac{32x^{4}}{(4x^{2} - 6x)^{2}} - \frac{96x^{3}}{(4x^{2} - 6x)^{2}} - \frac{12x^{2}}{(4x^{2} - 6x)} + \frac{58x^{2}}{(4x^{2} - 6x)^{2}} + \frac{18x}{(4x^{2} - 6x)} + \frac{45x}{(4x^{2} - 6x)^{2}} - \frac{1}{2(4x^{2} - 6x)} - \frac{36}{(4x^{2} - 6x)^{2}}\\ \end{split}\end{equation} \]

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