There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{({(2t + 1)}^{3})}{({(3t - 1)}^{4})})\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{8t^{3}}{(3t - 1)^{4}} + \frac{12t^{2}}{(3t - 1)^{4}} + \frac{6t}{(3t - 1)^{4}} + \frac{1}{(3t - 1)^{4}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{8t^{3}}{(3t - 1)^{4}} + \frac{12t^{2}}{(3t - 1)^{4}} + \frac{6t}{(3t - 1)^{4}} + \frac{1}{(3t - 1)^{4}}\right)}{dt}\\=&8(\frac{-4(3 + 0)}{(3t - 1)^{5}})t^{3} + \frac{8*3t^{2}}{(3t - 1)^{4}} + 12(\frac{-4(3 + 0)}{(3t - 1)^{5}})t^{2} + \frac{12*2t}{(3t - 1)^{4}} + 6(\frac{-4(3 + 0)}{(3t - 1)^{5}})t + \frac{6}{(3t - 1)^{4}} + (\frac{-4(3 + 0)}{(3t - 1)^{5}})\\=&\frac{-96t^{3}}{(3t - 1)^{5}} + \frac{24t^{2}}{(3t - 1)^{4}} - \frac{144t^{2}}{(3t - 1)^{5}} + \frac{24t}{(3t - 1)^{4}} - \frac{72t}{(3t - 1)^{5}} - \frac{12}{(3t - 1)^{5}} + \frac{6}{(3t - 1)^{4}}\\ \end{split}\end{equation} \]

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