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

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