There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(x + 12)}{({x}^{2} + 144)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{(x^{2} + 144)} + \frac{12}{(x^{2} + 144)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{(x^{2} + 144)} + \frac{12}{(x^{2} + 144)}\right)}{dx}\\=&(\frac{-(2x + 0)}{(x^{2} + 144)^{2}})x + \frac{1}{(x^{2} + 144)} + 12(\frac{-(2x + 0)}{(x^{2} + 144)^{2}})\\=&\frac{-2x^{2}}{(x^{2} + 144)^{2}} - \frac{24x}{(x^{2} + 144)^{2}} + \frac{1}{(x^{2} + 144)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2x^{2}}{(x^{2} + 144)^{2}} - \frac{24x}{(x^{2} + 144)^{2}} + \frac{1}{(x^{2} + 144)}\right)}{dx}\\=&-2(\frac{-2(2x + 0)}{(x^{2} + 144)^{3}})x^{2} - \frac{2*2x}{(x^{2} + 144)^{2}} - 24(\frac{-2(2x + 0)}{(x^{2} + 144)^{3}})x - \frac{24}{(x^{2} + 144)^{2}} + (\frac{-(2x + 0)}{(x^{2} + 144)^{2}})\\=&\frac{8x^{3}}{(x^{2} + 144)^{3}} - \frac{6x}{(x^{2} + 144)^{2}} + \frac{96x^{2}}{(x^{2} + 144)^{3}} - \frac{24}{(x^{2} + 144)^{2}}\\ \end{split}\end{equation} \]

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