There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -54x{\frac{1}{(9x + 1)}}^{2} - (2x - 2){\frac{1}{(x + 1)}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-54x}{(9x + 1)^{2}} - \frac{2x}{(x + 1)^{2}} + \frac{2}{(x + 1)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-54x}{(9x + 1)^{2}} - \frac{2x}{(x + 1)^{2}} + \frac{2}{(x + 1)^{2}}\right)}{dx}\\=&-54(\frac{-2(9 + 0)}{(9x + 1)^{3}})x - \frac{54}{(9x + 1)^{2}} - 2(\frac{-2(1 + 0)}{(x + 1)^{3}})x - \frac{2}{(x + 1)^{2}} + 2(\frac{-2(1 + 0)}{(x + 1)^{3}})\\=&\frac{972x}{(9x + 1)^{3}} + \frac{4x}{(x + 1)^{3}} - \frac{4}{(x + 1)^{3}} - \frac{2}{(x + 1)^{2}} - \frac{54}{(9x + 1)^{2}}\\ \end{split}\end{equation} \]

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