There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({t}^{2}(3t + 2))}{(1 + t)}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3t^{3}}{(t + 1)} + \frac{2t^{2}}{(t + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{3t^{3}}{(t + 1)} + \frac{2t^{2}}{(t + 1)}\right)}{dt}\\=&3(\frac{-(1 + 0)}{(t + 1)^{2}})t^{3} + \frac{3*3t^{2}}{(t + 1)} + 2(\frac{-(1 + 0)}{(t + 1)^{2}})t^{2} + \frac{2*2t}{(t + 1)}\\=&\frac{-3t^{3}}{(t + 1)^{2}} + \frac{9t^{2}}{(t + 1)} - \frac{2t^{2}}{(t + 1)^{2}} + \frac{4t}{(t + 1)}\\ \end{split}\end{equation} \]

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