There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{({x}^{3} + x + 2)}{({x}^{4} - 4{X}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(x^{4} - 4X^{2})} + \frac{x}{(x^{4} - 4X^{2})} + \frac{2}{(x^{4} - 4X^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(x^{4} - 4X^{2})} + \frac{x}{(x^{4} - 4X^{2})} + \frac{2}{(x^{4} - 4X^{2})}\right)}{dx}\\=&(\frac{-(4x^{3} + 0)}{(x^{4} - 4X^{2})^{2}})x^{3} + \frac{3x^{2}}{(x^{4} - 4X^{2})} + (\frac{-(4x^{3} + 0)}{(x^{4} - 4X^{2})^{2}})x + \frac{1}{(x^{4} - 4X^{2})} + 2(\frac{-(4x^{3} + 0)}{(x^{4} - 4X^{2})^{2}})\\=&\frac{-4x^{6}}{(x^{4} - 4X^{2})^{2}} + \frac{3x^{2}}{(x^{4} - 4X^{2})} - \frac{4x^{4}}{(x^{4} - 4X^{2})^{2}} - \frac{8x^{3}}{(x^{4} - 4X^{2})^{2}} + \frac{1}{(x^{4} - 4X^{2})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4x^{6}}{(x^{4} - 4X^{2})^{2}} + \frac{3x^{2}}{(x^{4} - 4X^{2})} - \frac{4x^{4}}{(x^{4} - 4X^{2})^{2}} - \frac{8x^{3}}{(x^{4} - 4X^{2})^{2}} + \frac{1}{(x^{4} - 4X^{2})}\right)}{dx}\\=&-4(\frac{-2(4x^{3} + 0)}{(x^{4} - 4X^{2})^{3}})x^{6} - \frac{4*6x^{5}}{(x^{4} - 4X^{2})^{2}} + 3(\frac{-(4x^{3} + 0)}{(x^{4} - 4X^{2})^{2}})x^{2} + \frac{3*2x}{(x^{4} - 4X^{2})} - 4(\frac{-2(4x^{3} + 0)}{(x^{4} - 4X^{2})^{3}})x^{4} - \frac{4*4x^{3}}{(x^{4} - 4X^{2})^{2}} - 8(\frac{-2(4x^{3} + 0)}{(x^{4} - 4X^{2})^{3}})x^{3} - \frac{8*3x^{2}}{(x^{4} - 4X^{2})^{2}} + (\frac{-(4x^{3} + 0)}{(x^{4} - 4X^{2})^{2}})\\=&\frac{32x^{9}}{(x^{4} - 4X^{2})^{3}} - \frac{36x^{5}}{(x^{4} - 4X^{2})^{2}} + \frac{6x}{(x^{4} - 4X^{2})} + \frac{32x^{7}}{(x^{4} - 4X^{2})^{3}} - \frac{20x^{3}}{(x^{4} - 4X^{2})^{2}} + \frac{64x^{6}}{(x^{4} - 4X^{2})^{3}} - \frac{24x^{2}}{(x^{4} - 4X^{2})^{2}}\\ \end{split}\end{equation} \]

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