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

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