There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{3} + \frac{3{x}^{2}(x + 1)}{(2{x}^{2} + 4x + 2)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{3} + \frac{3x^{3}}{(2x^{2} + 4x + 2)} + \frac{3x^{2}}{(2x^{2} + 4x + 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{3} + \frac{3x^{3}}{(2x^{2} + 4x + 2)} + \frac{3x^{2}}{(2x^{2} + 4x + 2)}\right)}{dx}\\=&3x^{2} + 3(\frac{-(2*2x + 4 + 0)}{(2x^{2} + 4x + 2)^{2}})x^{3} + \frac{3*3x^{2}}{(2x^{2} + 4x + 2)} + 3(\frac{-(2*2x + 4 + 0)}{(2x^{2} + 4x + 2)^{2}})x^{2} + \frac{3*2x}{(2x^{2} + 4x + 2)}\\=&3x^{2} - \frac{12x^{4}}{(2x^{2} + 4x + 2)^{2}} - \frac{24x^{3}}{(2x^{2} + 4x + 2)^{2}} + \frac{9x^{2}}{(2x^{2} + 4x + 2)} - \frac{12x^{2}}{(2x^{2} + 4x + 2)^{2}} + \frac{6x}{(2x^{2} + 4x + 2)}\\ \end{split}\end{equation} \]

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