There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {({x}^{2} + 3)}^{(\frac{2}{3})}{(3x + 2)}^{2}{(x + 1)}^{(\frac{-1}{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{9(x^{2} + 3)^{\frac{2}{3}}x^{2}}{(x + 1)^{\frac{1}{2}}} + \frac{12(x^{2} + 3)^{\frac{2}{3}}x}{(x + 1)^{\frac{1}{2}}} + \frac{4(x^{2} + 3)^{\frac{2}{3}}}{(x + 1)^{\frac{1}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{9(x^{2} + 3)^{\frac{2}{3}}x^{2}}{(x + 1)^{\frac{1}{2}}} + \frac{12(x^{2} + 3)^{\frac{2}{3}}x}{(x + 1)^{\frac{1}{2}}} + \frac{4(x^{2} + 3)^{\frac{2}{3}}}{(x + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{9(\frac{\frac{2}{3}(2x + 0)}{(x^{2} + 3)^{\frac{1}{3}}})x^{2}}{(x + 1)^{\frac{1}{2}}} + 9(x^{2} + 3)^{\frac{2}{3}}(\frac{\frac{-1}{2}(1 + 0)}{(x + 1)^{\frac{3}{2}}})x^{2} + \frac{9(x^{2} + 3)^{\frac{2}{3}}*2x}{(x + 1)^{\frac{1}{2}}} + \frac{12(\frac{\frac{2}{3}(2x + 0)}{(x^{2} + 3)^{\frac{1}{3}}})x}{(x + 1)^{\frac{1}{2}}} + 12(x^{2} + 3)^{\frac{2}{3}}(\frac{\frac{-1}{2}(1 + 0)}{(x + 1)^{\frac{3}{2}}})x + \frac{12(x^{2} + 3)^{\frac{2}{3}}}{(x + 1)^{\frac{1}{2}}} + \frac{4(\frac{\frac{2}{3}(2x + 0)}{(x^{2} + 3)^{\frac{1}{3}}})}{(x + 1)^{\frac{1}{2}}} + 4(x^{2} + 3)^{\frac{2}{3}}(\frac{\frac{-1}{2}(1 + 0)}{(x + 1)^{\frac{3}{2}}})\\=&\frac{12x^{3}}{(x^{2} + 3)^{\frac{1}{3}}(x + 1)^{\frac{1}{2}}} - \frac{9(x^{2} + 3)^{\frac{2}{3}}x^{2}}{2(x + 1)^{\frac{3}{2}}} + \frac{18(x^{2} + 3)^{\frac{2}{3}}x}{(x + 1)^{\frac{1}{2}}} + \frac{16x^{2}}{(x^{2} + 3)^{\frac{1}{3}}(x + 1)^{\frac{1}{2}}} - \frac{6(x^{2} + 3)^{\frac{2}{3}}x}{(x + 1)^{\frac{3}{2}}} + \frac{16x}{3(x^{2} + 3)^{\frac{1}{3}}(x + 1)^{\frac{1}{2}}} + \frac{12(x^{2} + 3)^{\frac{2}{3}}}{(x + 1)^{\frac{1}{2}}} - \frac{2(x^{2} + 3)^{\frac{2}{3}}}{(x + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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