There are 1 questions in this calculation: for each question, the 1 derivative of s is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({s}^{2} + 2s + 2)}{({s}^{2} + 4s)}\ with\ respect\ to\ s：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{s^{2}}{(s^{2} + 4s)} + \frac{2s}{(s^{2} + 4s)} + \frac{2}{(s^{2} + 4s)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{s^{2}}{(s^{2} + 4s)} + \frac{2s}{(s^{2} + 4s)} + \frac{2}{(s^{2} + 4s)}\right)}{ds}\\=&(\frac{-(2s + 4)}{(s^{2} + 4s)^{2}})s^{2} + \frac{2s}{(s^{2} + 4s)} + 2(\frac{-(2s + 4)}{(s^{2} + 4s)^{2}})s + \frac{2}{(s^{2} + 4s)} + 2(\frac{-(2s + 4)}{(s^{2} + 4s)^{2}})\\=&\frac{-2s^{3}}{(s^{2} + 4s)^{2}} - \frac{8s^{2}}{(s^{2} + 4s)^{2}} + \frac{2s}{(s^{2} + 4s)} - \frac{12s}{(s^{2} + 4s)^{2}} + \frac{2}{(s^{2} + 4s)} - \frac{8}{(s^{2} + 4s)^{2}}\\ \end{split}\end{equation} \]

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