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

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