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

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