There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(64{x}^{4} + 72{x}^{2} + 9)}{(32{x}^{3} + 12x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{64x^{4}}{(32x^{3} + 12x)} + \frac{72x^{2}}{(32x^{3} + 12x)} + \frac{9}{(32x^{3} + 12x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{64x^{4}}{(32x^{3} + 12x)} + \frac{72x^{2}}{(32x^{3} + 12x)} + \frac{9}{(32x^{3} + 12x)}\right)}{dx}\\=&64(\frac{-(32*3x^{2} + 12)}{(32x^{3} + 12x)^{2}})x^{4} + \frac{64*4x^{3}}{(32x^{3} + 12x)} + 72(\frac{-(32*3x^{2} + 12)}{(32x^{3} + 12x)^{2}})x^{2} + \frac{72*2x}{(32x^{3} + 12x)} + 9(\frac{-(32*3x^{2} + 12)}{(32x^{3} + 12x)^{2}})\\=&\frac{-6144x^{6}}{(32x^{3} + 12x)^{2}} - \frac{7680x^{4}}{(32x^{3} + 12x)^{2}} + \frac{256x^{3}}{(32x^{3} + 12x)} - \frac{1728x^{2}}{(32x^{3} + 12x)^{2}} + \frac{144x}{(32x^{3} + 12x)} - \frac{108}{(32x^{3} + 12x)^{2}}\\ \end{split}\end{equation} \]

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