There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln({(2x + 1)}^{4}{\frac{1}{(3x - 1)}}^{4})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})\right)}{dx}\\=&\frac{(16(\frac{-4(3 + 0)}{(3x - 1)^{5}})x^{4} + \frac{16*4x^{3}}{(3x - 1)^{4}} + 32(\frac{-4(3 + 0)}{(3x - 1)^{5}})x^{3} + \frac{32*3x^{2}}{(3x - 1)^{4}} + 24(\frac{-4(3 + 0)}{(3x - 1)^{5}})x^{2} + \frac{24*2x}{(3x - 1)^{4}} + 8(\frac{-4(3 + 0)}{(3x - 1)^{5}})x + \frac{8}{(3x - 1)^{4}} + (\frac{-4(3 + 0)}{(3x - 1)^{5}}))}{(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})}\\=&\frac{-192x^{4}}{(3x - 1)^{5}(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})} + \frac{64x^{3}}{(3x - 1)^{4}(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})} - \frac{384x^{3}}{(3x - 1)^{5}(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})} + \frac{96x^{2}}{(3x - 1)^{4}(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})} - \frac{288x^{2}}{(3x - 1)^{5}(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})} + \frac{48x}{(3x - 1)^{4}(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})} - \frac{96x}{(3x - 1)^{5}(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})} - \frac{12}{(3x - 1)^{5}(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})} + \frac{8}{(\frac{16x^{4}}{(3x - 1)^{4}} + \frac{32x^{3}}{(3x - 1)^{4}} + \frac{24x^{2}}{(3x - 1)^{4}} + \frac{8x}{(3x - 1)^{4}} + \frac{1}{(3x - 1)^{4}})(3x - 1)^{4}}\\ \end{split}\end{equation} \]

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