There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{({x}^{2} + 1)}{(1 + {x}^{4})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(x^{4} + 1)} + \frac{1}{(x^{4} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(x^{4} + 1)} + \frac{1}{(x^{4} + 1)}\right)}{dx}\\=&(\frac{-(4x^{3} + 0)}{(x^{4} + 1)^{2}})x^{2} + \frac{2x}{(x^{4} + 1)} + (\frac{-(4x^{3} + 0)}{(x^{4} + 1)^{2}})\\=&\frac{-4x^{5}}{(x^{4} + 1)^{2}} + \frac{2x}{(x^{4} + 1)} - \frac{4x^{3}}{(x^{4} + 1)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4x^{5}}{(x^{4} + 1)^{2}} + \frac{2x}{(x^{4} + 1)} - \frac{4x^{3}}{(x^{4} + 1)^{2}}\right)}{dx}\\=&-4(\frac{-2(4x^{3} + 0)}{(x^{4} + 1)^{3}})x^{5} - \frac{4*5x^{4}}{(x^{4} + 1)^{2}} + 2(\frac{-(4x^{3} + 0)}{(x^{4} + 1)^{2}})x + \frac{2}{(x^{4} + 1)} - 4(\frac{-2(4x^{3} + 0)}{(x^{4} + 1)^{3}})x^{3} - \frac{4*3x^{2}}{(x^{4} + 1)^{2}}\\=&\frac{32x^{8}}{(x^{4} + 1)^{3}} - \frac{28x^{4}}{(x^{4} + 1)^{2}} + \frac{32x^{6}}{(x^{4} + 1)^{3}} - \frac{12x^{2}}{(x^{4} + 1)^{2}} + \frac{2}{(x^{4} + 1)}\\ \end{split}\end{equation} \]

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