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

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