There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ arctan(18{x}^{20} + 6x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arctan(18x^{20} + 6x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(18x^{20} + 6x)\right)}{dx}\\=&(\frac{(18*20x^{19} + 6)}{(1 + (18x^{20} + 6x)^{2})})\\=&\frac{360x^{19}}{(324x^{40} + 216x^{21} + 36x^{2} + 1)} + \frac{6}{(324x^{40} + 216x^{21} + 36x^{2} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{360x^{19}}{(324x^{40} + 216x^{21} + 36x^{2} + 1)} + \frac{6}{(324x^{40} + 216x^{21} + 36x^{2} + 1)}\right)}{dx}\\=&360(\frac{-(324*40x^{39} + 216*21x^{20} + 36*2x + 0)}{(324x^{40} + 216x^{21} + 36x^{2} + 1)^{2}})x^{19} + \frac{360*19x^{18}}{(324x^{40} + 216x^{21} + 36x^{2} + 1)} + 6(\frac{-(324*40x^{39} + 216*21x^{20} + 36*2x + 0)}{(324x^{40} + 216x^{21} + 36x^{2} + 1)^{2}})\\=&\frac{-4665600x^{58}}{(324x^{40} + 216x^{21} + 36x^{2} + 1)^{2}} - \frac{1710720x^{39}}{(324x^{40} + 216x^{21} + 36x^{2} + 1)^{2}} - \frac{53136x^{20}}{(324x^{40} + 216x^{21} + 36x^{2} + 1)^{2}} + \frac{6840x^{18}}{(324x^{40} + 216x^{21} + 36x^{2} + 1)} - \frac{432x}{(324x^{40} + 216x^{21} + 36x^{2} + 1)^{2}}\\ \end{split}\end{equation} \]

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