There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({(2x + 1)}^{2}{(2 - 3x)}^{\frac{1}{3}})}{sqrt(x + 2)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{4(-3x + 2)^{\frac{1}{3}}x^{2}}{sqrt(x + 2)} + \frac{4(-3x + 2)^{\frac{1}{3}}x}{sqrt(x + 2)} + \frac{(-3x + 2)^{\frac{1}{3}}}{sqrt(x + 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{4(-3x + 2)^{\frac{1}{3}}x^{2}}{sqrt(x + 2)} + \frac{4(-3x + 2)^{\frac{1}{3}}x}{sqrt(x + 2)} + \frac{(-3x + 2)^{\frac{1}{3}}}{sqrt(x + 2)}\right)}{dx}\\=&\frac{4(\frac{\frac{1}{3}(-3 + 0)}{(-3x + 2)^{\frac{2}{3}}})x^{2}}{sqrt(x + 2)} + \frac{4(-3x + 2)^{\frac{1}{3}}*2x}{sqrt(x + 2)} + \frac{4(-3x + 2)^{\frac{1}{3}}x^{2}*-(1 + 0)*\frac{1}{2}}{(x + 2)(x + 2)^{\frac{1}{2}}} + \frac{4(\frac{\frac{1}{3}(-3 + 0)}{(-3x + 2)^{\frac{2}{3}}})x}{sqrt(x + 2)} + \frac{4(-3x + 2)^{\frac{1}{3}}}{sqrt(x + 2)} + \frac{4(-3x + 2)^{\frac{1}{3}}x*-(1 + 0)*\frac{1}{2}}{(x + 2)(x + 2)^{\frac{1}{2}}} + \frac{(\frac{\frac{1}{3}(-3 + 0)}{(-3x + 2)^{\frac{2}{3}}})}{sqrt(x + 2)} + \frac{(-3x + 2)^{\frac{1}{3}}*-(1 + 0)*\frac{1}{2}}{(x + 2)(x + 2)^{\frac{1}{2}}}\\=&\frac{-4x^{2}}{(-3x + 2)^{\frac{2}{3}}sqrt(x + 2)} + \frac{8(-3x + 2)^{\frac{1}{3}}x}{sqrt(x + 2)} - \frac{2(-3x + 2)^{\frac{1}{3}}x^{2}}{(x + 2)^{\frac{3}{2}}} - \frac{4x}{(-3x + 2)^{\frac{2}{3}}sqrt(x + 2)} + \frac{4(-3x + 2)^{\frac{1}{3}}}{sqrt(x + 2)} - \frac{2(-3x + 2)^{\frac{1}{3}}x}{(x + 2)^{\frac{3}{2}}} - \frac{1}{(-3x + 2)^{\frac{2}{3}}sqrt(x + 2)} - \frac{(-3x + 2)^{\frac{1}{3}}}{2(x + 2)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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