There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(\frac{({x}^{2} + 3x + 3)}{({x}^{2} - x + 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{x^{2}}{(x^{2} - x + 1)} + \frac{3x}{(x^{2} - x + 1)} + \frac{3}{(x^{2} - x + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{x^{2}}{(x^{2} - x + 1)} + \frac{3x}{(x^{2} - x + 1)} + \frac{3}{(x^{2} - x + 1)})\right)}{dx}\\=&\frac{((\frac{-(2x - 1 + 0)}{(x^{2} - x + 1)^{2}})x^{2} + \frac{2x}{(x^{2} - x + 1)} + 3(\frac{-(2x - 1 + 0)}{(x^{2} - x + 1)^{2}})x + \frac{3}{(x^{2} - x + 1)} + 3(\frac{-(2x - 1 + 0)}{(x^{2} - x + 1)^{2}}))*\frac{1}{2}}{(\frac{x^{2}}{(x^{2} - x + 1)} + \frac{3x}{(x^{2} - x + 1)} + \frac{3}{(x^{2} - x + 1)})^{\frac{1}{2}}}\\=&\frac{-x^{3}}{(x^{2} - x + 1)^{2}(\frac{x^{2}}{(x^{2} - x + 1)} + \frac{3x}{(x^{2} - x + 1)} + \frac{3}{(x^{2} - x + 1)})^{\frac{1}{2}}} - \frac{5x^{2}}{2(x^{2} - x + 1)^{2}(\frac{x^{2}}{(x^{2} - x + 1)} + \frac{3x}{(x^{2} - x + 1)} + \frac{3}{(x^{2} - x + 1)})^{\frac{1}{2}}} + \frac{x}{(x^{2} - x + 1)(\frac{x^{2}}{(x^{2} - x + 1)} + \frac{3x}{(x^{2} - x + 1)} + \frac{3}{(x^{2} - x + 1)})^{\frac{1}{2}}} - \frac{3x}{2(x^{2} - x + 1)^{2}(\frac{x^{2}}{(x^{2} - x + 1)} + \frac{3x}{(x^{2} - x + 1)} + \frac{3}{(x^{2} - x + 1)})^{\frac{1}{2}}} + \frac{3}{2(x^{2} - x + 1)(\frac{x^{2}}{(x^{2} - x + 1)} + \frac{3x}{(x^{2} - x + 1)} + \frac{3}{(x^{2} - x + 1)})^{\frac{1}{2}}} + \frac{3}{2(x^{2} - x + 1)^{2}(\frac{x^{2}}{(x^{2} - x + 1)} + \frac{3x}{(x^{2} - x + 1)} + \frac{3}{(x^{2} - x + 1)})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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