There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{35x}{(1 + 5x + 35{x}^{2} + \frac{497}{2}{x}^{3})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{35x}{(5x + 35x^{2} + \frac{497}{2}x^{3} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{35x}{(5x + 35x^{2} + \frac{497}{2}x^{3} + 1)}\right)}{dx}\\=&35(\frac{-(5 + 35*2x + \frac{497}{2}*3x^{2} + 0)}{(5x + 35x^{2} + \frac{497}{2}x^{3} + 1)^{2}})x + \frac{35}{(5x + 35x^{2} + \frac{497}{2}x^{3} + 1)}\\=& - \frac{2450x^{2}}{(5x + 35x^{2} + \frac{497}{2}x^{3} + 1)^{2}} - \frac{52185x^{3}}{2(5x + 35x^{2} + \frac{497}{2}x^{3} + 1)^{2}} - \frac{175x}{(5x + 35x^{2} + \frac{497}{2}x^{3} + 1)^{2}} + \frac{35}{(5x + 35x^{2} + \frac{497}{2}x^{3} + 1)}\\ \end{split}\end{equation} \]

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