There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(10 + 0.4x + 0.01{x}^{2})}{(4 + 0.1x + 0.01{x}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{0.4x}{(0.1x + 0.01x + 4)} + \frac{0.01x^{2}}{(0.1x + 0.01x + 4)} + \frac{10}{(0.1x + 0.01x + 4)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{0.4x}{(0.1x + 0.01x + 4)} + \frac{0.01x^{2}}{(0.1x + 0.01x + 4)} + \frac{10}{(0.1x + 0.01x + 4)}\right)}{dx}\\=&0.4(\frac{-(0.1 + 0.01 + 0)}{(0.1x + 0.01x + 4)^{2}})x + \frac{0.4}{(0.1x + 0.01x + 4)} + 0.01(\frac{-(0.1 + 0.01 + 0)}{(0.1x + 0.01x + 4)^{2}})x^{2} + \frac{0.01*2x}{(0.1x + 0.01x + 4)} + 10(\frac{-(0.1 + 0.01 + 0)}{(0.1x + 0.01x + 4)^{2}})\\=&\frac{-0.044x}{(0.1x + 0.01x + 4)(0.1x + 0.01x + 4)} - \frac{0.0011x^{2}}{(0.1x + 0.01x + 4)(0.1x + 0.01x + 4)} + \frac{0.02x}{(0.1x + 0.01x + 4)} - \frac{1.1}{(0.1x + 0.01x + 4)(0.1x + 0.01x + 4)} + \frac{0.4}{(0.1x + 0.01x + 4)}\\ \end{split}\end{equation} \]

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