There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{(2x - 6)}^{4}}{({(x + 2)}^{3})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{16x^{4}}{(x + 2)^{3}} - \frac{192x^{3}}{(x + 2)^{3}} + \frac{864x^{2}}{(x + 2)^{3}} - \frac{1728x}{(x + 2)^{3}} + \frac{1296}{(x + 2)^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{16x^{4}}{(x + 2)^{3}} - \frac{192x^{3}}{(x + 2)^{3}} + \frac{864x^{2}}{(x + 2)^{3}} - \frac{1728x}{(x + 2)^{3}} + \frac{1296}{(x + 2)^{3}}\right)}{dx}\\=&16(\frac{-3(1 + 0)}{(x + 2)^{4}})x^{4} + \frac{16*4x^{3}}{(x + 2)^{3}} - 192(\frac{-3(1 + 0)}{(x + 2)^{4}})x^{3} - \frac{192*3x^{2}}{(x + 2)^{3}} + 864(\frac{-3(1 + 0)}{(x + 2)^{4}})x^{2} + \frac{864*2x}{(x + 2)^{3}} - 1728(\frac{-3(1 + 0)}{(x + 2)^{4}})x - \frac{1728}{(x + 2)^{3}} + 1296(\frac{-3(1 + 0)}{(x + 2)^{4}})\\=&\frac{-48x^{4}}{(x + 2)^{4}} + \frac{64x^{3}}{(x + 2)^{3}} + \frac{576x^{3}}{(x + 2)^{4}} - \frac{576x^{2}}{(x + 2)^{3}} - \frac{2592x^{2}}{(x + 2)^{4}} + \frac{1728x}{(x + 2)^{3}} + \frac{5184x}{(x + 2)^{4}} - \frac{3888}{(x + 2)^{4}} - \frac{1728}{(x + 2)^{3}}\\ \end{split}\end{equation} \]

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