There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1.1x - 0.1{x}^{2})}{(-0.2{x}^{2} + 0.2x + 0.01)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1.1x}{(-0.2x^{2} + 0.2x + 0.01)} - \frac{0.1x^{2}}{(-0.2x^{2} + 0.2x + 0.01)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1.1x}{(-0.2x^{2} + 0.2x + 0.01)} - \frac{0.1x^{2}}{(-0.2x^{2} + 0.2x + 0.01)}\right)}{dx}\\=&1.1(\frac{-(-0.2*2x + 0.2 + 0)}{(-0.2x^{2} + 0.2x + 0.01)^{2}})x + \frac{1.1}{(-0.2x^{2} + 0.2x + 0.01)} - 0.1(\frac{-(-0.2*2x + 0.2 + 0)}{(-0.2x^{2} + 0.2x + 0.01)^{2}})x^{2} - \frac{0.1*2x}{(-0.2x^{2} + 0.2x + 0.01)}\\=&\frac{0.44x^{2}}{(-0.2x^{2} + 0.2x + 0.01)(-0.2x^{2} + 0.2x + 0.01)} - \frac{0.22x}{(-0.2x^{2} + 0.2x + 0.01)(-0.2x^{2} + 0.2x + 0.01)} - \frac{0.04x^{3}}{(-0.2x^{2} + 0.2x + 0.01)(-0.2x^{2} + 0.2x + 0.01)} + \frac{0.02x^{2}}{(-0.2x^{2} + 0.2x + 0.01)(-0.2x^{2} + 0.2x + 0.01)} - \frac{0.2x}{(-0.2x^{2} + 0.2x + 0.01)} + \frac{1.1}{(-0.2x^{2} + 0.2x + 0.01)}\\ \end{split}\end{equation} \]

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