There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 1 - 2xarcsin(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - 2xarcsin(x) + 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - 2xarcsin(x) + 1\right)}{dx}\\=& - 2arcsin(x) - 2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}) + 0\\=& - 2arcsin(x) - \frac{2x}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - 2arcsin(x) - \frac{2x}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=& - 2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}) - 2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}}\\=& - \frac{2x^{2}}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{2x^{2}}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=& - 2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x^{2} - \frac{2*2x}{(-x^{2} + 1)^{\frac{3}{2}}} - 2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}) - 2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})\\=& - \frac{6x^{3}}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{8x}{(-x^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{6x^{3}}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{8x}{(-x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=& - 6(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{3} - \frac{6*3x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}} - 8(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x - \frac{8}{(-x^{2} + 1)^{\frac{3}{2}}}\\=& - \frac{30x^{4}}{(-x^{2} + 1)^{\frac{7}{2}}} - \frac{42x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{8}{(-x^{2} + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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