There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(4{x}^{4} + 3{x}^{3} + 2{x}^{2} + x + 0)}{(2{x}^{2} + x + 0)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{4x^{4}}{(2x^{2} + x)} + \frac{3x^{3}}{(2x^{2} + x)} + \frac{2x^{2}}{(2x^{2} + x)} + \frac{x}{(2x^{2} + x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{4x^{4}}{(2x^{2} + x)} + \frac{3x^{3}}{(2x^{2} + x)} + \frac{2x^{2}}{(2x^{2} + x)} + \frac{x}{(2x^{2} + x)}\right)}{dx}\\=&4(\frac{-(2*2x + 1)}{(2x^{2} + x)^{2}})x^{4} + \frac{4*4x^{3}}{(2x^{2} + x)} + 3(\frac{-(2*2x + 1)}{(2x^{2} + x)^{2}})x^{3} + \frac{3*3x^{2}}{(2x^{2} + x)} + 2(\frac{-(2*2x + 1)}{(2x^{2} + x)^{2}})x^{2} + \frac{2*2x}{(2x^{2} + x)} + (\frac{-(2*2x + 1)}{(2x^{2} + x)^{2}})x + \frac{1}{(2x^{2} + x)}\\=&\frac{-16x^{5}}{(2x^{2} + x)^{2}} - \frac{16x^{4}}{(2x^{2} + x)^{2}} + \frac{16x^{3}}{(2x^{2} + x)} - \frac{11x^{3}}{(2x^{2} + x)^{2}} - \frac{6x^{2}}{(2x^{2} + x)^{2}} + \frac{9x^{2}}{(2x^{2} + x)} + \frac{4x}{(2x^{2} + x)} - \frac{x}{(2x^{2} + x)^{2}} + \frac{1}{(2x^{2} + x)}\\ \end{split}\end{equation} \]

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