There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(580{x}^{4} + 490{x}^{2} - 420{x}^{3} - 420x + 90)}{(14x - 3)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{580x^{4}}{(14x - 3)} + \frac{490x^{2}}{(14x - 3)} - \frac{420x^{3}}{(14x - 3)} - \frac{420x}{(14x - 3)} + \frac{90}{(14x - 3)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{580x^{4}}{(14x - 3)} + \frac{490x^{2}}{(14x - 3)} - \frac{420x^{3}}{(14x - 3)} - \frac{420x}{(14x - 3)} + \frac{90}{(14x - 3)}\right)}{dx}\\=&580(\frac{-(14 + 0)}{(14x - 3)^{2}})x^{4} + \frac{580*4x^{3}}{(14x - 3)} + 490(\frac{-(14 + 0)}{(14x - 3)^{2}})x^{2} + \frac{490*2x}{(14x - 3)} - 420(\frac{-(14 + 0)}{(14x - 3)^{2}})x^{3} - \frac{420*3x^{2}}{(14x - 3)} - 420(\frac{-(14 + 0)}{(14x - 3)^{2}})x - \frac{420}{(14x - 3)} + 90(\frac{-(14 + 0)}{(14x - 3)^{2}})\\=&\frac{-8120x^{4}}{(14x - 3)^{2}} + \frac{2320x^{3}}{(14x - 3)} - \frac{6860x^{2}}{(14x - 3)^{2}} + \frac{980x}{(14x - 3)} + \frac{5880x^{3}}{(14x - 3)^{2}} - \frac{1260x^{2}}{(14x - 3)} + \frac{5880x}{(14x - 3)^{2}} - \frac{1260}{(14x - 3)^{2}} - \frac{420}{(14x - 3)}\\ \end{split}\end{equation} \]

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