There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(2x - 4{x}^{2} + (\frac{4}{3}){x}^{3})}^{2}e^{-2k}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 4x^{2}e^{-2k} - 16x^{3}e^{-2k} + \frac{64}{3}x^{4}e^{-2k} - \frac{32}{3}x^{5}e^{-2k} + \frac{16}{9}x^{6}e^{-2k}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 4x^{2}e^{-2k} - 16x^{3}e^{-2k} + \frac{64}{3}x^{4}e^{-2k} - \frac{32}{3}x^{5}e^{-2k} + \frac{16}{9}x^{6}e^{-2k}\right)}{dx}\\=&4*2xe^{-2k} + 4x^{2}e^{-2k}*0 - 16*3x^{2}e^{-2k} - 16x^{3}e^{-2k}*0 + \frac{64}{3}*4x^{3}e^{-2k} + \frac{64}{3}x^{4}e^{-2k}*0 - \frac{32}{3}*5x^{4}e^{-2k} - \frac{32}{3}x^{5}e^{-2k}*0 + \frac{16}{9}*6x^{5}e^{-2k} + \frac{16}{9}x^{6}e^{-2k}*0\\=&8xe^{-2k} - 48x^{2}e^{-2k} + \frac{256x^{3}e^{-2k}}{3} - \frac{160x^{4}e^{-2k}}{3} + \frac{32x^{5}e^{-2k}}{3}\\ \end{split}\end{equation} \]

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