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

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