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

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