There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(({(x + 1)}^{\frac{1}{2}})({(1 - x)}^{2}))}{({(x - 2)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(x + 1)^{\frac{1}{2}}x^{2}}{(x - 2)^{2}} - \frac{2(x + 1)^{\frac{1}{2}}x}{(x - 2)^{2}} + \frac{(x + 1)^{\frac{1}{2}}}{(x - 2)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(x + 1)^{\frac{1}{2}}x^{2}}{(x - 2)^{2}} - \frac{2(x + 1)^{\frac{1}{2}}x}{(x - 2)^{2}} + \frac{(x + 1)^{\frac{1}{2}}}{(x - 2)^{2}}\right)}{dx}\\=&(\frac{-2(1 + 0)}{(x - 2)^{3}})(x + 1)^{\frac{1}{2}}x^{2} + \frac{(\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}})x^{2}}{(x - 2)^{2}} + \frac{(x + 1)^{\frac{1}{2}}*2x}{(x - 2)^{2}} - 2(\frac{-2(1 + 0)}{(x - 2)^{3}})(x + 1)^{\frac{1}{2}}x - \frac{2(\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}})x}{(x - 2)^{2}} - \frac{2(x + 1)^{\frac{1}{2}}}{(x - 2)^{2}} + (\frac{-2(1 + 0)}{(x - 2)^{3}})(x + 1)^{\frac{1}{2}} + \frac{(\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}})}{(x - 2)^{2}}\\=&\frac{-2(x + 1)^{\frac{1}{2}}x^{2}}{(x - 2)^{3}} + \frac{x^{2}}{2(x + 1)^{\frac{1}{2}}(x - 2)^{2}} + \frac{2(x + 1)^{\frac{1}{2}}x}{(x - 2)^{2}} + \frac{4(x + 1)^{\frac{1}{2}}x}{(x - 2)^{3}} - \frac{x}{(x + 1)^{\frac{1}{2}}(x - 2)^{2}} - \frac{2(x + 1)^{\frac{1}{2}}}{(x - 2)^{3}} - \frac{2(x + 1)^{\frac{1}{2}}}{(x - 2)^{2}} + \frac{1}{2(x + 1)^{\frac{1}{2}}(x - 2)^{2}}\\ \end{split}\end{equation} \]

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