There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(x - 4)*2{(x + 1)}^{\frac{1}{3}}}{3} + {(X + 1)}^{(\frac{2}{3})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2}{3}(x + 1)^{\frac{1}{3}}x - \frac{8}{3}(x + 1)^{\frac{1}{3}} + (X + 1)^{\frac{2}{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2}{3}(x + 1)^{\frac{1}{3}}x - \frac{8}{3}(x + 1)^{\frac{1}{3}} + (X + 1)^{\frac{2}{3}}\right)}{dx}\\=&\frac{2}{3}(\frac{\frac{1}{3}(1 + 0)}{(x + 1)^{\frac{2}{3}}})x + \frac{2}{3}(x + 1)^{\frac{1}{3}} - \frac{8}{3}(\frac{\frac{1}{3}(1 + 0)}{(x + 1)^{\frac{2}{3}}}) + (\frac{\frac{2}{3}(0 + 0)}{(X + 1)^{\frac{1}{3}}})\\=&\frac{2x}{9(x + 1)^{\frac{2}{3}}} + \frac{2(x + 1)^{\frac{1}{3}}}{3} - \frac{8}{9(x + 1)^{\frac{2}{3}}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！