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

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