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

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