There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {(9 - x)}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (-x + 9)^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (-x + 9)^{x}\right)}{dx}\\=&((-x + 9)^{x}((1)ln(-x + 9) + \frac{(x)(-1 + 0)}{(-x + 9)}))\\=&(-x + 9)^{x}ln(-x + 9) - \frac{x(-x + 9)^{x}}{(-x + 9)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( (-x + 9)^{x}ln(-x + 9) - \frac{x(-x + 9)^{x}}{(-x + 9)}\right)}{dx}\\=&((-x + 9)^{x}((1)ln(-x + 9) + \frac{(x)(-1 + 0)}{(-x + 9)}))ln(-x + 9) + \frac{(-x + 9)^{x}(-1 + 0)}{(-x + 9)} - (\frac{-(-1 + 0)}{(-x + 9)^{2}})x(-x + 9)^{x} - \frac{(-x + 9)^{x}}{(-x + 9)} - \frac{x((-x + 9)^{x}((1)ln(-x + 9) + \frac{(x)(-1 + 0)}{(-x + 9)}))}{(-x + 9)}\\=&(-x + 9)^{x}ln^{2}(-x + 9) - \frac{2x(-x + 9)^{x}ln(-x + 9)}{(-x + 9)} - \frac{2(-x + 9)^{x}}{(-x + 9)} - \frac{x(-x + 9)^{x}}{(-x + 9)^{2}} + \frac{x^{2}(-x + 9)^{x}}{(-x + 9)^{2}}\\ \end{split}\end{equation} \]

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