There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(-{x}^{2} + 5x + 50)}{(170 + 10x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-x^{2}}{(10x + 170)} + \frac{5x}{(10x + 170)} + \frac{50}{(10x + 170)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-x^{2}}{(10x + 170)} + \frac{5x}{(10x + 170)} + \frac{50}{(10x + 170)}\right)}{dx}\\=&-(\frac{-(10 + 0)}{(10x + 170)^{2}})x^{2} - \frac{2x}{(10x + 170)} + 5(\frac{-(10 + 0)}{(10x + 170)^{2}})x + \frac{5}{(10x + 170)} + 50(\frac{-(10 + 0)}{(10x + 170)^{2}})\\=&\frac{10x^{2}}{(10x + 170)^{2}} - \frac{2x}{(10x + 170)} - \frac{50x}{(10x + 170)^{2}} - \frac{500}{(10x + 170)^{2}} + \frac{5}{(10x + 170)}\\ \end{split}\end{equation} \]

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