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

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