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

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