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

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