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

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