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

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