There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(x + 1)}^{2}{(3x - 2)}^{\frac{1}{3}}{\frac{1}{(x + 7)}}^{(\frac{2}{3})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(3x - 2)^{\frac{1}{3}}x^{2}}{(x + 7)^{\frac{2}{3}}} + \frac{2(3x - 2)^{\frac{1}{3}}x}{(x + 7)^{\frac{2}{3}}} + \frac{(3x - 2)^{\frac{1}{3}}}{(x + 7)^{\frac{2}{3}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(3x - 2)^{\frac{1}{3}}x^{2}}{(x + 7)^{\frac{2}{3}}} + \frac{2(3x - 2)^{\frac{1}{3}}x}{(x + 7)^{\frac{2}{3}}} + \frac{(3x - 2)^{\frac{1}{3}}}{(x + 7)^{\frac{2}{3}}}\right)}{dx}\\=&\frac{(\frac{\frac{1}{3}(3 + 0)}{(3x - 2)^{\frac{2}{3}}})x^{2}}{(x + 7)^{\frac{2}{3}}} + (3x - 2)^{\frac{1}{3}}(\frac{\frac{-2}{3}(1 + 0)}{(x + 7)^{\frac{5}{3}}})x^{2} + \frac{(3x - 2)^{\frac{1}{3}}*2x}{(x + 7)^{\frac{2}{3}}} + \frac{2(\frac{\frac{1}{3}(3 + 0)}{(3x - 2)^{\frac{2}{3}}})x}{(x + 7)^{\frac{2}{3}}} + 2(3x - 2)^{\frac{1}{3}}(\frac{\frac{-2}{3}(1 + 0)}{(x + 7)^{\frac{5}{3}}})x + \frac{2(3x - 2)^{\frac{1}{3}}}{(x + 7)^{\frac{2}{3}}} + \frac{(\frac{\frac{1}{3}(3 + 0)}{(3x - 2)^{\frac{2}{3}}})}{(x + 7)^{\frac{2}{3}}} + (3x - 2)^{\frac{1}{3}}(\frac{\frac{-2}{3}(1 + 0)}{(x + 7)^{\frac{5}{3}}})\\=&\frac{x^{2}}{(3x - 2)^{\frac{2}{3}}(x + 7)^{\frac{2}{3}}} - \frac{2(3x - 2)^{\frac{1}{3}}x^{2}}{3(x + 7)^{\frac{5}{3}}} + \frac{2(3x - 2)^{\frac{1}{3}}x}{(x + 7)^{\frac{2}{3}}} + \frac{2x}{(3x - 2)^{\frac{2}{3}}(x + 7)^{\frac{2}{3}}} - \frac{4(3x - 2)^{\frac{1}{3}}x}{3(x + 7)^{\frac{5}{3}}} + \frac{2(3x - 2)^{\frac{1}{3}}}{(x + 7)^{\frac{2}{3}}} + \frac{1}{(3x - 2)^{\frac{2}{3}}(x + 7)^{\frac{2}{3}}} - \frac{2(3x - 2)^{\frac{1}{3}}}{3(x + 7)^{\frac{5}{3}}}\\ \end{split}\end{equation} \]

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