There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{(x + 1)}^{1}{(2 - x)}^{3}{\frac{1}{(x - 1)}}^{4}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{-1}{2}x^{4}}{(x - 1)^{4}} + \frac{\frac{5}{2}x^{3}}{(x - 1)^{4}} - \frac{3x^{2}}{(x - 1)^{4}} - \frac{2x}{(x - 1)^{4}} + \frac{4}{(x - 1)^{4}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{-1}{2}x^{4}}{(x - 1)^{4}} + \frac{\frac{5}{2}x^{3}}{(x - 1)^{4}} - \frac{3x^{2}}{(x - 1)^{4}} - \frac{2x}{(x - 1)^{4}} + \frac{4}{(x - 1)^{4}}\right)}{dx}\\=&\frac{-1}{2}(\frac{-4(1 + 0)}{(x - 1)^{5}})x^{4} - \frac{\frac{1}{2}*4x^{3}}{(x - 1)^{4}} + \frac{5}{2}(\frac{-4(1 + 0)}{(x - 1)^{5}})x^{3} + \frac{\frac{5}{2}*3x^{2}}{(x - 1)^{4}} - 3(\frac{-4(1 + 0)}{(x - 1)^{5}})x^{2} - \frac{3*2x}{(x - 1)^{4}} - 2(\frac{-4(1 + 0)}{(x - 1)^{5}})x - \frac{2}{(x - 1)^{4}} + 4(\frac{-4(1 + 0)}{(x - 1)^{5}})\\=&\frac{2x^{4}}{(x - 1)^{5}} - \frac{2x^{3}}{(x - 1)^{4}} - \frac{10x^{3}}{(x - 1)^{5}} + \frac{15x^{2}}{2(x - 1)^{4}} + \frac{12x^{2}}{(x - 1)^{5}} - \frac{6x}{(x - 1)^{4}} + \frac{8x}{(x - 1)^{5}} - \frac{16}{(x - 1)^{5}} - \frac{2}{(x - 1)^{4}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！