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

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