There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-4x(y{(x)}^{2} + {x}^{2})(x)}{y(4{x}^{2} + 9y(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-4x^{4}}{(4x^{2} + 9yx)} - \frac{4x^{4}}{(4x^{2} + 9yx)y}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-4x^{4}}{(4x^{2} + 9yx)} - \frac{4x^{4}}{(4x^{2} + 9yx)y}\right)}{dx}\\=&-4(\frac{-(4*2x + 9y)}{(4x^{2} + 9yx)^{2}})x^{4} - \frac{4*4x^{3}}{(4x^{2} + 9yx)} - \frac{4(\frac{-(4*2x + 9y)}{(4x^{2} + 9yx)^{2}})x^{4}}{y} - \frac{4*4x^{3}}{(4x^{2} + 9yx)y}\\=&\frac{32x^{5}}{(4x^{2} + 9yx)^{2}} + \frac{32x^{5}}{(4x^{2} + 9yx)^{2}y} - \frac{16x^{3}}{(4x^{2} + 9yx)} + \frac{36yx^{4}}{(4x^{2} + 9yx)^{2}} + \frac{36x^{4}}{(4x^{2} + 9yx)^{2}} - \frac{16x^{3}}{(4x^{2} + 9yx)y}\\ \end{split}\end{equation} \]

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