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

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