There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(4{x}^{5} + 3{x}^{4} + 2{x}^{2} + x)}{({x}^{2} + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{4x^{5}}{(x^{2} + 1)} + \frac{3x^{4}}{(x^{2} + 1)} + \frac{2x^{2}}{(x^{2} + 1)} + \frac{x}{(x^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{4x^{5}}{(x^{2} + 1)} + \frac{3x^{4}}{(x^{2} + 1)} + \frac{2x^{2}}{(x^{2} + 1)} + \frac{x}{(x^{2} + 1)}\right)}{dx}\\=&4(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x^{5} + \frac{4*5x^{4}}{(x^{2} + 1)} + 3(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x^{4} + \frac{3*4x^{3}}{(x^{2} + 1)} + 2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x^{2} + \frac{2*2x}{(x^{2} + 1)} + (\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x + \frac{1}{(x^{2} + 1)}\\=&\frac{-8x^{6}}{(x^{2} + 1)^{2}} + \frac{20x^{4}}{(x^{2} + 1)} - \frac{6x^{5}}{(x^{2} + 1)^{2}} + \frac{12x^{3}}{(x^{2} + 1)} - \frac{4x^{3}}{(x^{2} + 1)^{2}} + \frac{4x}{(x^{2} + 1)} - \frac{2x^{2}}{(x^{2} + 1)^{2}} + \frac{1}{(x^{2} + 1)}\\ \end{split}\end{equation} \]

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