There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(-{x}^{2} + Ax + B)}{({x}^{2} + 2)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-x^{2}}{(x^{2} + 2)} + \frac{Ax}{(x^{2} + 2)} + \frac{B}{(x^{2} + 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-x^{2}}{(x^{2} + 2)} + \frac{Ax}{(x^{2} + 2)} + \frac{B}{(x^{2} + 2)}\right)}{dx}\\=&-(\frac{-(2x + 0)}{(x^{2} + 2)^{2}})x^{2} - \frac{2x}{(x^{2} + 2)} + (\frac{-(2x + 0)}{(x^{2} + 2)^{2}})Ax + \frac{A}{(x^{2} + 2)} + (\frac{-(2x + 0)}{(x^{2} + 2)^{2}})B + 0\\=&\frac{2x^{3}}{(x^{2} + 2)^{2}} - \frac{2x}{(x^{2} + 2)} - \frac{2Ax^{2}}{(x^{2} + 2)^{2}} + \frac{A}{(x^{2} + 2)} - \frac{2Bx}{(x^{2} + 2)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2x^{3}}{(x^{2} + 2)^{2}} - \frac{2x}{(x^{2} + 2)} - \frac{2Ax^{2}}{(x^{2} + 2)^{2}} + \frac{A}{(x^{2} + 2)} - \frac{2Bx}{(x^{2} + 2)^{2}}\right)}{dx}\\=&2(\frac{-2(2x + 0)}{(x^{2} + 2)^{3}})x^{3} + \frac{2*3x^{2}}{(x^{2} + 2)^{2}} - 2(\frac{-(2x + 0)}{(x^{2} + 2)^{2}})x - \frac{2}{(x^{2} + 2)} - 2(\frac{-2(2x + 0)}{(x^{2} + 2)^{3}})Ax^{2} - \frac{2A*2x}{(x^{2} + 2)^{2}} + (\frac{-(2x + 0)}{(x^{2} + 2)^{2}})A + 0 - 2(\frac{-2(2x + 0)}{(x^{2} + 2)^{3}})Bx - \frac{2B}{(x^{2} + 2)^{2}}\\=&\frac{-8x^{4}}{(x^{2} + 2)^{3}} + \frac{10x^{2}}{(x^{2} + 2)^{2}} + \frac{8Bx^{2}}{(x^{2} + 2)^{3}} + \frac{8Ax^{3}}{(x^{2} + 2)^{3}} - \frac{6Ax}{(x^{2} + 2)^{2}} - \frac{2B}{(x^{2} + 2)^{2}} - \frac{2}{(x^{2} + 2)}\\ \end{split}\end{equation} \]

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