There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(5{x}^{4} + 6{x}^{3} + 7{x}^{2} + 8x + 3)}{(4{x}^{2} + 2x + 5)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{5x^{4}}{(4x^{2} + 2x + 5)} + \frac{6x^{3}}{(4x^{2} + 2x + 5)} + \frac{7x^{2}}{(4x^{2} + 2x + 5)} + \frac{8x}{(4x^{2} + 2x + 5)} + \frac{3}{(4x^{2} + 2x + 5)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{5x^{4}}{(4x^{2} + 2x + 5)} + \frac{6x^{3}}{(4x^{2} + 2x + 5)} + \frac{7x^{2}}{(4x^{2} + 2x + 5)} + \frac{8x}{(4x^{2} + 2x + 5)} + \frac{3}{(4x^{2} + 2x + 5)}\right)}{dx}\\=&5(\frac{-(4*2x + 2 + 0)}{(4x^{2} + 2x + 5)^{2}})x^{4} + \frac{5*4x^{3}}{(4x^{2} + 2x + 5)} + 6(\frac{-(4*2x + 2 + 0)}{(4x^{2} + 2x + 5)^{2}})x^{3} + \frac{6*3x^{2}}{(4x^{2} + 2x + 5)} + 7(\frac{-(4*2x + 2 + 0)}{(4x^{2} + 2x + 5)^{2}})x^{2} + \frac{7*2x}{(4x^{2} + 2x + 5)} + 8(\frac{-(4*2x + 2 + 0)}{(4x^{2} + 2x + 5)^{2}})x + \frac{8}{(4x^{2} + 2x + 5)} + 3(\frac{-(4*2x + 2 + 0)}{(4x^{2} + 2x + 5)^{2}})\\=&\frac{-40x^{5}}{(4x^{2} + 2x + 5)^{2}} - \frac{58x^{4}}{(4x^{2} + 2x + 5)^{2}} + \frac{20x^{3}}{(4x^{2} + 2x + 5)} - \frac{68x^{3}}{(4x^{2} + 2x + 5)^{2}} - \frac{78x^{2}}{(4x^{2} + 2x + 5)^{2}} + \frac{18x^{2}}{(4x^{2} + 2x + 5)} + \frac{14x}{(4x^{2} + 2x + 5)} - \frac{40x}{(4x^{2} + 2x + 5)^{2}} + \frac{8}{(4x^{2} + 2x + 5)} - \frac{6}{(4x^{2} + 2x + 5)^{2}}\\ \end{split}\end{equation} \]

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