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

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