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

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