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

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