There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ \frac{(3{x}^{4} - 6{x}^{3} + 4{x}^{2} - 1)}{(x{(1 - x)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3x^{3}}{(-x + 1)^{2}} - \frac{6x^{2}}{(-x + 1)^{2}} + \frac{4x}{(-x + 1)^{2}} - \frac{1}{(-x + 1)^{2}x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{3x^{3}}{(-x + 1)^{2}} - \frac{6x^{2}}{(-x + 1)^{2}} + \frac{4x}{(-x + 1)^{2}} - \frac{1}{(-x + 1)^{2}x}\right)}{dx}\\=&3(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{3} + \frac{3*3x^{2}}{(-x + 1)^{2}} - 6(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2} - \frac{6*2x}{(-x + 1)^{2}} + 4(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x + \frac{4}{(-x + 1)^{2}} - \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{x} - \frac{-1}{(-x + 1)^{2}x^{2}}\\=&\frac{6x^{3}}{(-x + 1)^{3}} + \frac{9x^{2}}{(-x + 1)^{2}} - \frac{12x^{2}}{(-x + 1)^{3}} - \frac{12x}{(-x + 1)^{2}} + \frac{8x}{(-x + 1)^{3}} - \frac{2}{(-x + 1)^{3}x} + \frac{1}{(-x + 1)^{2}x^{2}} + \frac{4}{(-x + 1)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{6x^{3}}{(-x + 1)^{3}} + \frac{9x^{2}}{(-x + 1)^{2}} - \frac{12x^{2}}{(-x + 1)^{3}} - \frac{12x}{(-x + 1)^{2}} + \frac{8x}{(-x + 1)^{3}} - \frac{2}{(-x + 1)^{3}x} + \frac{1}{(-x + 1)^{2}x^{2}} + \frac{4}{(-x + 1)^{2}}\right)}{dx}\\=&6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{3} + \frac{6*3x^{2}}{(-x + 1)^{3}} + 9(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{2} + \frac{9*2x}{(-x + 1)^{2}} - 12(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{2} - \frac{12*2x}{(-x + 1)^{3}} - 12(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x - \frac{12}{(-x + 1)^{2}} + 8(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x + \frac{8}{(-x + 1)^{3}} - \frac{2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{x} - \frac{2*-1}{(-x + 1)^{3}x^{2}} + \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{x^{2}} + \frac{-2}{(-x + 1)^{2}x^{3}} + 4(\frac{-2(-1 + 0)}{(-x + 1)^{3}})\\=&\frac{18x^{3}}{(-x + 1)^{4}} + \frac{36x^{2}}{(-x + 1)^{3}} + \frac{18x}{(-x + 1)^{2}} - \frac{36x^{2}}{(-x + 1)^{4}} - \frac{48x}{(-x + 1)^{3}} + \frac{24x}{(-x + 1)^{4}} - \frac{6}{(-x + 1)^{4}x} + \frac{4}{(-x + 1)^{3}x^{2}} - \frac{2}{(-x + 1)^{2}x^{3}} + \frac{16}{(-x + 1)^{3}} - \frac{12}{(-x + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{18x^{3}}{(-x + 1)^{4}} + \frac{36x^{2}}{(-x + 1)^{3}} + \frac{18x}{(-x + 1)^{2}} - \frac{36x^{2}}{(-x + 1)^{4}} - \frac{48x}{(-x + 1)^{3}} + \frac{24x}{(-x + 1)^{4}} - \frac{6}{(-x + 1)^{4}x} + \frac{4}{(-x + 1)^{3}x^{2}} - \frac{2}{(-x + 1)^{2}x^{3}} + \frac{16}{(-x + 1)^{3}} - \frac{12}{(-x + 1)^{2}}\right)}{dx}\\=&18(\frac{-4(-1 + 0)}{(-x + 1)^{5}})x^{3} + \frac{18*3x^{2}}{(-x + 1)^{4}} + 36(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{2} + \frac{36*2x}{(-x + 1)^{3}} + 18(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x + \frac{18}{(-x + 1)^{2}} - 36(\frac{-4(-1 + 0)}{(-x + 1)^{5}})x^{2} - \frac{36*2x}{(-x + 1)^{4}} - 48(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x - \frac{48}{(-x + 1)^{3}} + 24(\frac{-4(-1 + 0)}{(-x + 1)^{5}})x + \frac{24}{(-x + 1)^{4}} - \frac{6(\frac{-4(-1 + 0)}{(-x + 1)^{5}})}{x} - \frac{6*-1}{(-x + 1)^{4}x^{2}} + \frac{4(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{x^{2}} + \frac{4*-2}{(-x + 1)^{3}x^{3}} - \frac{2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{x^{3}} - \frac{2*-3}{(-x + 1)^{2}x^{4}} + 16(\frac{-3(-1 + 0)}{(-x + 1)^{4}}) - 12(\frac{-2(-1 + 0)}{(-x + 1)^{3}})\\=&\frac{72x^{3}}{(-x + 1)^{5}} + \frac{162x^{2}}{(-x + 1)^{4}} + \frac{108x}{(-x + 1)^{3}} - \frac{144x^{2}}{(-x + 1)^{5}} - \frac{216x}{(-x + 1)^{4}} + \frac{96x}{(-x + 1)^{5}} - \frac{24}{(-x + 1)^{5}x} + \frac{18}{(-x + 1)^{4}x^{2}} - \frac{12}{(-x + 1)^{3}x^{3}} + \frac{6}{(-x + 1)^{2}x^{4}} - \frac{72}{(-x + 1)^{3}} + \frac{72}{(-x + 1)^{4}} + \frac{18}{(-x + 1)^{2}}\\ \end{split}\end{equation} \]

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