There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ arctan(\frac{4}{x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(\frac{4}{x})\right)}{dx}\\=&(\frac{(\frac{4*-1}{x^{2}})}{(1 + (\frac{4}{x})^{2})})\\=&\frac{-4}{(\frac{16}{x^{2}} + 1)x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4}{(\frac{16}{x^{2}} + 1)x^{2}}\right)}{dx}\\=&\frac{-4(\frac{-(\frac{16*-2}{x^{3}} + 0)}{(\frac{16}{x^{2}} + 1)^{2}})}{x^{2}} - \frac{4*-2}{(\frac{16}{x^{2}} + 1)x^{3}}\\=&\frac{-128}{(\frac{16}{x^{2}} + 1)^{2}x^{5}} + \frac{8}{(\frac{16}{x^{2}} + 1)x^{3}}\\ \end{split}\end{equation} \]

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