There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{{(1 - x)}^{3}}{(27(2x + 1))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-x^{3}}{(54x + 27)} + \frac{3x^{2}}{(54x + 27)} - \frac{3x}{(54x + 27)} + \frac{1}{(54x + 27)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-x^{3}}{(54x + 27)} + \frac{3x^{2}}{(54x + 27)} - \frac{3x}{(54x + 27)} + \frac{1}{(54x + 27)}\right)}{dx}\\=&-(\frac{-(54 + 0)}{(54x + 27)^{2}})x^{3} - \frac{3x^{2}}{(54x + 27)} + 3(\frac{-(54 + 0)}{(54x + 27)^{2}})x^{2} + \frac{3*2x}{(54x + 27)} - 3(\frac{-(54 + 0)}{(54x + 27)^{2}})x - \frac{3}{(54x + 27)} + (\frac{-(54 + 0)}{(54x + 27)^{2}})\\=&\frac{54x^{3}}{(54x + 27)^{2}} - \frac{3x^{2}}{(54x + 27)} - \frac{162x^{2}}{(54x + 27)^{2}} + \frac{6x}{(54x + 27)} + \frac{162x}{(54x + 27)^{2}} - \frac{54}{(54x + 27)^{2}} - \frac{3}{(54x + 27)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{54x^{3}}{(54x + 27)^{2}} - \frac{3x^{2}}{(54x + 27)} - \frac{162x^{2}}{(54x + 27)^{2}} + \frac{6x}{(54x + 27)} + \frac{162x}{(54x + 27)^{2}} - \frac{54}{(54x + 27)^{2}} - \frac{3}{(54x + 27)}\right)}{dx}\\=&54(\frac{-2(54 + 0)}{(54x + 27)^{3}})x^{3} + \frac{54*3x^{2}}{(54x + 27)^{2}} - 3(\frac{-(54 + 0)}{(54x + 27)^{2}})x^{2} - \frac{3*2x}{(54x + 27)} - 162(\frac{-2(54 + 0)}{(54x + 27)^{3}})x^{2} - \frac{162*2x}{(54x + 27)^{2}} + 6(\frac{-(54 + 0)}{(54x + 27)^{2}})x + \frac{6}{(54x + 27)} + 162(\frac{-2(54 + 0)}{(54x + 27)^{3}})x + \frac{162}{(54x + 27)^{2}} - 54(\frac{-2(54 + 0)}{(54x + 27)^{3}}) - 3(\frac{-(54 + 0)}{(54x + 27)^{2}})\\=&\frac{-5832x^{3}}{(54x + 27)^{3}} + \frac{324x^{2}}{(54x + 27)^{2}} - \frac{6x}{(54x + 27)} + \frac{17496x^{2}}{(54x + 27)^{3}} - \frac{648x}{(54x + 27)^{2}} - \frac{17496x}{(54x + 27)^{3}} + \frac{5832}{(54x + 27)^{3}} + \frac{324}{(54x + 27)^{2}} + \frac{6}{(54x + 27)}\\ \end{split}\end{equation} \]

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