There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(4{x}^{3}{(-16 + 4x)}^{5})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(4096x^{8} - 81920x^{7} + 655360x^{6} - 2621440x^{5} + 5242880x^{4} - 4194304x^{3})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(4096x^{8} - 81920x^{7} + 655360x^{6} - 2621440x^{5} + 5242880x^{4} - 4194304x^{3})\right)}{dx}\\=&\frac{(4096*8x^{7} - 81920*7x^{6} + 655360*6x^{5} - 2621440*5x^{4} + 5242880*4x^{3} - 4194304*3x^{2})}{(4096x^{8} - 81920x^{7} + 655360x^{6} - 2621440x^{5} + 5242880x^{4} - 4194304x^{3})}\\=&\frac{32768x^{7}}{(4096x^{8} - 81920x^{7} + 655360x^{6} - 2621440x^{5} + 5242880x^{4} - 4194304x^{3})} - \frac{573440x^{6}}{(4096x^{8} - 81920x^{7} + 655360x^{6} - 2621440x^{5} + 5242880x^{4} - 4194304x^{3})} + \frac{3932160x^{5}}{(4096x^{8} - 81920x^{7} + 655360x^{6} - 2621440x^{5} + 5242880x^{4} - 4194304x^{3})} - \frac{13107200x^{4}}{(4096x^{8} - 81920x^{7} + 655360x^{6} - 2621440x^{5} + 5242880x^{4} - 4194304x^{3})} + \frac{20971520x^{3}}{(4096x^{8} - 81920x^{7} + 655360x^{6} - 2621440x^{5} + 5242880x^{4} - 4194304x^{3})} - \frac{12582912x^{2}}{(4096x^{8} - 81920x^{7} + 655360x^{6} - 2621440x^{5} + 5242880x^{4} - 4194304x^{3})}\\ \end{split}\end{equation} \]

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