There are 1 questions in this calculation: for each question, the 1 derivative of s is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{s(s + 3)({s}^{2} + 2s + 2)}{(s + 2)}\ with\ respect\ to\ s：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{s^{4}}{(s + 2)} + \frac{5s^{3}}{(s + 2)} + \frac{8s^{2}}{(s + 2)} + \frac{6s}{(s + 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{s^{4}}{(s + 2)} + \frac{5s^{3}}{(s + 2)} + \frac{8s^{2}}{(s + 2)} + \frac{6s}{(s + 2)}\right)}{ds}\\=&(\frac{-(1 + 0)}{(s + 2)^{2}})s^{4} + \frac{4s^{3}}{(s + 2)} + 5(\frac{-(1 + 0)}{(s + 2)^{2}})s^{3} + \frac{5*3s^{2}}{(s + 2)} + 8(\frac{-(1 + 0)}{(s + 2)^{2}})s^{2} + \frac{8*2s}{(s + 2)} + 6(\frac{-(1 + 0)}{(s + 2)^{2}})s + \frac{6}{(s + 2)}\\=&\frac{-s^{4}}{(s + 2)^{2}} + \frac{4s^{3}}{(s + 2)} - \frac{5s^{3}}{(s + 2)^{2}} + \frac{15s^{2}}{(s + 2)} - \frac{8s^{2}}{(s + 2)^{2}} + \frac{16s}{(s + 2)} - \frac{6s}{(s + 2)^{2}} + \frac{6}{(s + 2)}\\ \end{split}\end{equation} \]

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