There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ (6{x}^{2} + 6x){\frac{1}{({x}^{2} + x + 1)}}^{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{6x^{2}}{(x^{2} + x + 1)^{3}} + \frac{6x}{(x^{2} + x + 1)^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{6x^{2}}{(x^{2} + x + 1)^{3}} + \frac{6x}{(x^{2} + x + 1)^{3}}\right)}{dx}\\=&6(\frac{-3(2x + 1 + 0)}{(x^{2} + x + 1)^{4}})x^{2} + \frac{6*2x}{(x^{2} + x + 1)^{3}} + 6(\frac{-3(2x + 1 + 0)}{(x^{2} + x + 1)^{4}})x + \frac{6}{(x^{2} + x + 1)^{3}}\\=&\frac{-36x^{3}}{(x^{2} + x + 1)^{4}} - \frac{54x^{2}}{(x^{2} + x + 1)^{4}} + \frac{12x}{(x^{2} + x + 1)^{3}} - \frac{18x}{(x^{2} + x + 1)^{4}} + \frac{6}{(x^{2} + x + 1)^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-36x^{3}}{(x^{2} + x + 1)^{4}} - \frac{54x^{2}}{(x^{2} + x + 1)^{4}} + \frac{12x}{(x^{2} + x + 1)^{3}} - \frac{18x}{(x^{2} + x + 1)^{4}} + \frac{6}{(x^{2} + x + 1)^{3}}\right)}{dx}\\=&-36(\frac{-4(2x + 1 + 0)}{(x^{2} + x + 1)^{5}})x^{3} - \frac{36*3x^{2}}{(x^{2} + x + 1)^{4}} - 54(\frac{-4(2x + 1 + 0)}{(x^{2} + x + 1)^{5}})x^{2} - \frac{54*2x}{(x^{2} + x + 1)^{4}} + 12(\frac{-3(2x + 1 + 0)}{(x^{2} + x + 1)^{4}})x + \frac{12}{(x^{2} + x + 1)^{3}} - 18(\frac{-4(2x + 1 + 0)}{(x^{2} + x + 1)^{5}})x - \frac{18}{(x^{2} + x + 1)^{4}} + 6(\frac{-3(2x + 1 + 0)}{(x^{2} + x + 1)^{4}})\\=&\frac{288x^{4}}{(x^{2} + x + 1)^{5}} + \frac{576x^{3}}{(x^{2} + x + 1)^{5}} - \frac{180x^{2}}{(x^{2} + x + 1)^{4}} + \frac{360x^{2}}{(x^{2} + x + 1)^{5}} - \frac{180x}{(x^{2} + x + 1)^{4}} + \frac{72x}{(x^{2} + x + 1)^{5}} - \frac{36}{(x^{2} + x + 1)^{4}} + \frac{12}{(x^{2} + x + 1)^{3}}\\ \end{split}\end{equation} \]

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