There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ (3{x}^{4} - 6a{x}^{2} + 3{a}^{2}){\frac{1}{(3{x}^{2} + a)}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3x^{4}}{(3x^{2} + a)^{2}} - \frac{6ax^{2}}{(3x^{2} + a)^{2}} + \frac{3a^{2}}{(3x^{2} + a)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{3x^{4}}{(3x^{2} + a)^{2}} - \frac{6ax^{2}}{(3x^{2} + a)^{2}} + \frac{3a^{2}}{(3x^{2} + a)^{2}}\right)}{dx}\\=&3(\frac{-2(3*2x + 0)}{(3x^{2} + a)^{3}})x^{4} + \frac{3*4x^{3}}{(3x^{2} + a)^{2}} - 6(\frac{-2(3*2x + 0)}{(3x^{2} + a)^{3}})ax^{2} - \frac{6a*2x}{(3x^{2} + a)^{2}} + 3(\frac{-2(3*2x + 0)}{(3x^{2} + a)^{3}})a^{2} + 0\\=&\frac{-36x^{5}}{(3x^{2} + a)^{3}} + \frac{12x^{3}}{(3x^{2} + a)^{2}} + \frac{72ax^{3}}{(3x^{2} + a)^{3}} - \frac{12ax}{(3x^{2} + a)^{2}} - \frac{36a^{2}x}{(3x^{2} + a)^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-36x^{5}}{(3x^{2} + a)^{3}} + \frac{12x^{3}}{(3x^{2} + a)^{2}} + \frac{72ax^{3}}{(3x^{2} + a)^{3}} - \frac{12ax}{(3x^{2} + a)^{2}} - \frac{36a^{2}x}{(3x^{2} + a)^{3}}\right)}{dx}\\=&-36(\frac{-3(3*2x + 0)}{(3x^{2} + a)^{4}})x^{5} - \frac{36*5x^{4}}{(3x^{2} + a)^{3}} + 12(\frac{-2(3*2x + 0)}{(3x^{2} + a)^{3}})x^{3} + \frac{12*3x^{2}}{(3x^{2} + a)^{2}} + 72(\frac{-3(3*2x + 0)}{(3x^{2} + a)^{4}})ax^{3} + \frac{72a*3x^{2}}{(3x^{2} + a)^{3}} - 12(\frac{-2(3*2x + 0)}{(3x^{2} + a)^{3}})ax - \frac{12a}{(3x^{2} + a)^{2}} - 36(\frac{-3(3*2x + 0)}{(3x^{2} + a)^{4}})a^{2}x - \frac{36a^{2}}{(3x^{2} + a)^{3}}\\=&\frac{648x^{6}}{(3x^{2} + a)^{4}} - \frac{324x^{4}}{(3x^{2} + a)^{3}} + \frac{36x^{2}}{(3x^{2} + a)^{2}} - \frac{1296ax^{4}}{(3x^{2} + a)^{4}} + \frac{360ax^{2}}{(3x^{2} + a)^{3}} + \frac{648a^{2}x^{2}}{(3x^{2} + a)^{4}} - \frac{12a}{(3x^{2} + a)^{2}} - \frac{36a^{2}}{(3x^{2} + a)^{3}}\\ \end{split}\end{equation} \]

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