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

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