There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (12{x}^{4} - 6x){\frac{1}{({x}^{3} + 1)}}^{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{12x^{4}}{(x^{3} + 1)^{3}} - \frac{6x}{(x^{3} + 1)^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{12x^{4}}{(x^{3} + 1)^{3}} - \frac{6x}{(x^{3} + 1)^{3}}\right)}{dx}\\=&12(\frac{-3(3x^{2} + 0)}{(x^{3} + 1)^{4}})x^{4} + \frac{12*4x^{3}}{(x^{3} + 1)^{3}} - 6(\frac{-3(3x^{2} + 0)}{(x^{3} + 1)^{4}})x - \frac{6}{(x^{3} + 1)^{3}}\\=&\frac{-108x^{6}}{(x^{3} + 1)^{4}} + \frac{48x^{3}}{(x^{3} + 1)^{3}} + \frac{54x^{3}}{(x^{3} + 1)^{4}} - \frac{6}{(x^{3} + 1)^{3}}\\ \end{split}\end{equation} \]

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