There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(x + \frac{{({x}^{2} + 1)}^{2}}{1})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(x + x^{4} + 2x^{2} + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(x + x^{4} + 2x^{2} + 1)\right)}{dx}\\=&\frac{(1 + 4x^{3} + 2*2x + 0)}{(x + x^{4} + 2x^{2} + 1)}\\=&\frac{4x^{3}}{(x + x^{4} + 2x^{2} + 1)} + \frac{4x}{(x + x^{4} + 2x^{2} + 1)} + \frac{1}{(x + x^{4} + 2x^{2} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4x^{3}}{(x + x^{4} + 2x^{2} + 1)} + \frac{4x}{(x + x^{4} + 2x^{2} + 1)} + \frac{1}{(x + x^{4} + 2x^{2} + 1)}\right)}{dx}\\=&4(\frac{-(1 + 4x^{3} + 2*2x + 0)}{(x + x^{4} + 2x^{2} + 1)^{2}})x^{3} + \frac{4*3x^{2}}{(x + x^{4} + 2x^{2} + 1)} + 4(\frac{-(1 + 4x^{3} + 2*2x + 0)}{(x + x^{4} + 2x^{2} + 1)^{2}})x + \frac{4}{(x + x^{4} + 2x^{2} + 1)} + (\frac{-(1 + 4x^{3} + 2*2x + 0)}{(x + x^{4} + 2x^{2} + 1)^{2}})\\=&\frac{-16x^{6}}{(x + x^{4} + 2x^{2} + 1)^{2}} - \frac{32x^{4}}{(x + x^{4} + 2x^{2} + 1)^{2}} + \frac{12x^{2}}{(x + x^{4} + 2x^{2} + 1)} - \frac{16x^{2}}{(x + x^{4} + 2x^{2} + 1)^{2}} - \frac{8x^{3}}{(x + x^{4} + 2x^{2} + 1)^{2}} - \frac{8x}{(x + x^{4} + 2x^{2} + 1)^{2}} + \frac{4}{(x + x^{4} + 2x^{2} + 1)} - \frac{1}{(x + x^{4} + 2x^{2} + 1)^{2}}\\ \end{split}\end{equation} \]

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