There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2} - 10x + 24)}{({x}^{2} - 10x + 24 + 2x - 10)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(x^{2} - 8x + 14)} - \frac{10x}{(x^{2} - 8x + 14)} + \frac{24}{(x^{2} - 8x + 14)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(x^{2} - 8x + 14)} - \frac{10x}{(x^{2} - 8x + 14)} + \frac{24}{(x^{2} - 8x + 14)}\right)}{dx}\\=&(\frac{-(2x - 8 + 0)}{(x^{2} - 8x + 14)^{2}})x^{2} + \frac{2x}{(x^{2} - 8x + 14)} - 10(\frac{-(2x - 8 + 0)}{(x^{2} - 8x + 14)^{2}})x - \frac{10}{(x^{2} - 8x + 14)} + 24(\frac{-(2x - 8 + 0)}{(x^{2} - 8x + 14)^{2}})\\=&\frac{-2x^{3}}{(x^{2} - 8x + 14)^{2}} + \frac{28x^{2}}{(x^{2} - 8x + 14)^{2}} + \frac{2x}{(x^{2} - 8x + 14)} - \frac{128x}{(x^{2} - 8x + 14)^{2}} - \frac{10}{(x^{2} - 8x + 14)} + \frac{192}{(x^{2} - 8x + 14)^{2}}\\ \end{split}\end{equation} \]

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