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

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