There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{({x}^{5} + 43x)}{(12x + 3)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{5}}{(12x + 3)} + \frac{43x}{(12x + 3)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{5}}{(12x + 3)} + \frac{43x}{(12x + 3)}\right)}{dx}\\=&(\frac{-(12 + 0)}{(12x + 3)^{2}})x^{5} + \frac{5x^{4}}{(12x + 3)} + 43(\frac{-(12 + 0)}{(12x + 3)^{2}})x + \frac{43}{(12x + 3)}\\=&\frac{-12x^{5}}{(12x + 3)^{2}} + \frac{5x^{4}}{(12x + 3)} - \frac{516x}{(12x + 3)^{2}} + \frac{43}{(12x + 3)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-12x^{5}}{(12x + 3)^{2}} + \frac{5x^{4}}{(12x + 3)} - \frac{516x}{(12x + 3)^{2}} + \frac{43}{(12x + 3)}\right)}{dx}\\=&-12(\frac{-2(12 + 0)}{(12x + 3)^{3}})x^{5} - \frac{12*5x^{4}}{(12x + 3)^{2}} + 5(\frac{-(12 + 0)}{(12x + 3)^{2}})x^{4} + \frac{5*4x^{3}}{(12x + 3)} - 516(\frac{-2(12 + 0)}{(12x + 3)^{3}})x - \frac{516}{(12x + 3)^{2}} + 43(\frac{-(12 + 0)}{(12x + 3)^{2}})\\=&\frac{288x^{5}}{(12x + 3)^{3}} - \frac{120x^{4}}{(12x + 3)^{2}} + \frac{20x^{3}}{(12x + 3)} + \frac{12384x}{(12x + 3)^{3}} - \frac{1032}{(12x + 3)^{2}}\\ \end{split}\end{equation} \]

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