There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(x + 1)}^{\frac{1}{2}}{(2 - x)}^{3}{\frac{1}{(x - 1)}}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-(x + 1)^{\frac{1}{2}}x^{3}}{(x - 1)^{4}} + \frac{6(x + 1)^{\frac{1}{2}}x^{2}}{(x - 1)^{4}} - \frac{12(x + 1)^{\frac{1}{2}}x}{(x - 1)^{4}} + \frac{8(x + 1)^{\frac{1}{2}}}{(x - 1)^{4}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-(x + 1)^{\frac{1}{2}}x^{3}}{(x - 1)^{4}} + \frac{6(x + 1)^{\frac{1}{2}}x^{2}}{(x - 1)^{4}} - \frac{12(x + 1)^{\frac{1}{2}}x}{(x - 1)^{4}} + \frac{8(x + 1)^{\frac{1}{2}}}{(x - 1)^{4}}\right)}{dx}\\=&\frac{-(\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}})x^{3}}{(x - 1)^{4}} - (x + 1)^{\frac{1}{2}}(\frac{-4(1 + 0)}{(x - 1)^{5}})x^{3} - \frac{(x + 1)^{\frac{1}{2}}*3x^{2}}{(x - 1)^{4}} + \frac{6(\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}})x^{2}}{(x - 1)^{4}} + 6(x + 1)^{\frac{1}{2}}(\frac{-4(1 + 0)}{(x - 1)^{5}})x^{2} + \frac{6(x + 1)^{\frac{1}{2}}*2x}{(x - 1)^{4}} - \frac{12(\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}})x}{(x - 1)^{4}} - 12(x + 1)^{\frac{1}{2}}(\frac{-4(1 + 0)}{(x - 1)^{5}})x - \frac{12(x + 1)^{\frac{1}{2}}}{(x - 1)^{4}} + \frac{8(\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}})}{(x - 1)^{4}} + 8(x + 1)^{\frac{1}{2}}(\frac{-4(1 + 0)}{(x - 1)^{5}})\\=&\frac{-x^{3}}{2(x + 1)^{\frac{1}{2}}(x - 1)^{4}} + \frac{4(x + 1)^{\frac{1}{2}}x^{3}}{(x - 1)^{5}} - \frac{3(x + 1)^{\frac{1}{2}}x^{2}}{(x - 1)^{4}} + \frac{3x^{2}}{(x + 1)^{\frac{1}{2}}(x - 1)^{4}} - \frac{24(x + 1)^{\frac{1}{2}}x^{2}}{(x - 1)^{5}} + \frac{12(x + 1)^{\frac{1}{2}}x}{(x - 1)^{4}} - \frac{6x}{(x + 1)^{\frac{1}{2}}(x - 1)^{4}} + \frac{48(x + 1)^{\frac{1}{2}}x}{(x - 1)^{5}} - \frac{32(x + 1)^{\frac{1}{2}}}{(x - 1)^{5}} + \frac{4}{(x + 1)^{\frac{1}{2}}(x - 1)^{4}} - \frac{12(x + 1)^{\frac{1}{2}}}{(x - 1)^{4}}\\ \end{split}\end{equation} \]

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