There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{(4{x}^{2} - 1)}{({x}^{2} - 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{4x^{2}}{(x^{2} - 1)} - \frac{1}{(x^{2} - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{4x^{2}}{(x^{2} - 1)} - \frac{1}{(x^{2} - 1)}\right)}{dx}\\=&4(\frac{-(2x + 0)}{(x^{2} - 1)^{2}})x^{2} + \frac{4*2x}{(x^{2} - 1)} - (\frac{-(2x + 0)}{(x^{2} - 1)^{2}})\\=&\frac{-8x^{3}}{(x^{2} - 1)^{2}} + \frac{8x}{(x^{2} - 1)} + \frac{2x}{(x^{2} - 1)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-8x^{3}}{(x^{2} - 1)^{2}} + \frac{8x}{(x^{2} - 1)} + \frac{2x}{(x^{2} - 1)^{2}}\right)}{dx}\\=&-8(\frac{-2(2x + 0)}{(x^{2} - 1)^{3}})x^{3} - \frac{8*3x^{2}}{(x^{2} - 1)^{2}} + 8(\frac{-(2x + 0)}{(x^{2} - 1)^{2}})x + \frac{8}{(x^{2} - 1)} + 2(\frac{-2(2x + 0)}{(x^{2} - 1)^{3}})x + \frac{2}{(x^{2} - 1)^{2}}\\=&\frac{32x^{4}}{(x^{2} - 1)^{3}} - \frac{40x^{2}}{(x^{2} - 1)^{2}} - \frac{8x^{2}}{(x^{2} - 1)^{3}} + \frac{2}{(x^{2} - 1)^{2}} + \frac{8}{(x^{2} - 1)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{32x^{4}}{(x^{2} - 1)^{3}} - \frac{40x^{2}}{(x^{2} - 1)^{2}} - \frac{8x^{2}}{(x^{2} - 1)^{3}} + \frac{2}{(x^{2} - 1)^{2}} + \frac{8}{(x^{2} - 1)}\right)}{dx}\\=&32(\frac{-3(2x + 0)}{(x^{2} - 1)^{4}})x^{4} + \frac{32*4x^{3}}{(x^{2} - 1)^{3}} - 40(\frac{-2(2x + 0)}{(x^{2} - 1)^{3}})x^{2} - \frac{40*2x}{(x^{2} - 1)^{2}} - 8(\frac{-3(2x + 0)}{(x^{2} - 1)^{4}})x^{2} - \frac{8*2x}{(x^{2} - 1)^{3}} + 2(\frac{-2(2x + 0)}{(x^{2} - 1)^{3}}) + 8(\frac{-(2x + 0)}{(x^{2} - 1)^{2}})\\=&\frac{-192x^{5}}{(x^{2} - 1)^{4}} + \frac{288x^{3}}{(x^{2} - 1)^{3}} - \frac{96x}{(x^{2} - 1)^{2}} + \frac{48x^{3}}{(x^{2} - 1)^{4}} - \frac{24x}{(x^{2} - 1)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-192x^{5}}{(x^{2} - 1)^{4}} + \frac{288x^{3}}{(x^{2} - 1)^{3}} - \frac{96x}{(x^{2} - 1)^{2}} + \frac{48x^{3}}{(x^{2} - 1)^{4}} - \frac{24x}{(x^{2} - 1)^{3}}\right)}{dx}\\=&-192(\frac{-4(2x + 0)}{(x^{2} - 1)^{5}})x^{5} - \frac{192*5x^{4}}{(x^{2} - 1)^{4}} + 288(\frac{-3(2x + 0)}{(x^{2} - 1)^{4}})x^{3} + \frac{288*3x^{2}}{(x^{2} - 1)^{3}} - 96(\frac{-2(2x + 0)}{(x^{2} - 1)^{3}})x - \frac{96}{(x^{2} - 1)^{2}} + 48(\frac{-4(2x + 0)}{(x^{2} - 1)^{5}})x^{3} + \frac{48*3x^{2}}{(x^{2} - 1)^{4}} - 24(\frac{-3(2x + 0)}{(x^{2} - 1)^{4}})x - \frac{24}{(x^{2} - 1)^{3}}\\=&\frac{1536x^{6}}{(x^{2} - 1)^{5}} - \frac{2688x^{4}}{(x^{2} - 1)^{4}} + \frac{1248x^{2}}{(x^{2} - 1)^{3}} - \frac{384x^{4}}{(x^{2} - 1)^{5}} + \frac{288x^{2}}{(x^{2} - 1)^{4}} - \frac{24}{(x^{2} - 1)^{3}} - \frac{96}{(x^{2} - 1)^{2}}\\ \end{split}\end{equation} \]

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