There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(2x - 3)}^{20}{(2x + 2)}^{10}{\frac{1}{(2x + 1)}}^{30}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(2x - 3)^{20}(2x + 2)^{10}}{(2x + 1)^{30}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(2x - 3)^{20}(2x + 2)^{10}}{(2x + 1)^{30}}\right)}{dx}\\=&\frac{(20(2x - 3)^{19}(2 + 0))(2x + 2)^{10}}{(2x + 1)^{30}} + \frac{(2x - 3)^{20}(10(2x + 2)^{9}(2 + 0))}{(2x + 1)^{30}} + (2x - 3)^{20}(2x + 2)^{10}(\frac{-30(2 + 0)}{(2x + 1)^{31}})\\=&\frac{40(2x - 3)^{19}(2x + 2)^{10}}{(2x + 1)^{30}} + \frac{20(2x + 2)^{9}(2x - 3)^{20}}{(2x + 1)^{30}} - \frac{60(2x - 3)^{20}(2x + 2)^{10}}{(2x + 1)^{31}}\\ \end{split}\end{equation} \]

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