There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln({(2t + 1)}^{5}{\frac{1}{(3t - 1)}}^{4})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{32t^{5}}{(3t - 1)^{4}} + \frac{80t^{4}}{(3t - 1)^{4}} + \frac{80t^{3}}{(3t - 1)^{4}} + \frac{40t^{2}}{(3t - 1)^{4}} + \frac{10t}{(3t - 1)^{4}} + \frac{1}{(3t - 1)^{4}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{32t^{5}}{(3t - 1)^{4}} + \frac{80t^{4}}{(3t - 1)^{4}} + \frac{80t^{3}}{(3t - 1)^{4}} + \frac{40t^{2}}{(3t - 1)^{4}} + \frac{10t}{(3t - 1)^{4}} + \frac{1}{(3t - 1)^{4}})\right)}{dx}\\=&\frac{(32(\frac{-4(0 + 0)}{(3t - 1)^{5}})t^{5} + 0 + 80(\frac{-4(0 + 0)}{(3t - 1)^{5}})t^{4} + 0 + 80(\frac{-4(0 + 0)}{(3t - 1)^{5}})t^{3} + 0 + 40(\frac{-4(0 + 0)}{(3t - 1)^{5}})t^{2} + 0 + 10(\frac{-4(0 + 0)}{(3t - 1)^{5}})t + 0 + (\frac{-4(0 + 0)}{(3t - 1)^{5}}))}{(\frac{32t^{5}}{(3t - 1)^{4}} + \frac{80t^{4}}{(3t - 1)^{4}} + \frac{80t^{3}}{(3t - 1)^{4}} + \frac{40t^{2}}{(3t - 1)^{4}} + \frac{10t}{(3t - 1)^{4}} + \frac{1}{(3t - 1)^{4}})}\\=& - 0\\ \end{split}\end{equation} \]

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