There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(25000 + 3050x + 6{x}^{2})}{(500 + 3x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3050x}{(3x + 500)} + \frac{6x^{2}}{(3x + 500)} + \frac{25000}{(3x + 500)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{3050x}{(3x + 500)} + \frac{6x^{2}}{(3x + 500)} + \frac{25000}{(3x + 500)}\right)}{dx}\\=&3050(\frac{-(3 + 0)}{(3x + 500)^{2}})x + \frac{3050}{(3x + 500)} + 6(\frac{-(3 + 0)}{(3x + 500)^{2}})x^{2} + \frac{6*2x}{(3x + 500)} + 25000(\frac{-(3 + 0)}{(3x + 500)^{2}})\\=& - \frac{9150x}{(3x + 500)^{2}} - \frac{18x^{2}}{(3x + 500)^{2}} + \frac{12x}{(3x + 500)} - \frac{75000}{(3x + 500)^{2}} + \frac{3050}{(3x + 500)}\\ \end{split}\end{equation} \]

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