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

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