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

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