There are 1 questions in this calculation: for each question, the 4 derivative of X is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ arcsin(2X)\ with\ respect\ to\ X：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin(2X)\right)}{dX}\\=&(\frac{(2)}{((1 - (2X)^{2})^{\frac{1}{2}})})\\=&\frac{2}{(-4X^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2}{(-4X^{2} + 1)^{\frac{1}{2}}}\right)}{dX}\\=&2(\frac{\frac{-1}{2}(-4*2X + 0)}{(-4X^{2} + 1)^{\frac{3}{2}}})\\=&\frac{8X}{(-4X^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{8X}{(-4X^{2} + 1)^{\frac{3}{2}}}\right)}{dX}\\=&8(\frac{\frac{-3}{2}(-4*2X + 0)}{(-4X^{2} + 1)^{\frac{5}{2}}})X + \frac{8}{(-4X^{2} + 1)^{\frac{3}{2}}}\\=&\frac{96X^{2}}{(-4X^{2} + 1)^{\frac{5}{2}}} + \frac{8}{(-4X^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{96X^{2}}{(-4X^{2} + 1)^{\frac{5}{2}}} + \frac{8}{(-4X^{2} + 1)^{\frac{3}{2}}}\right)}{dX}\\=&96(\frac{\frac{-5}{2}(-4*2X + 0)}{(-4X^{2} + 1)^{\frac{7}{2}}})X^{2} + \frac{96*2X}{(-4X^{2} + 1)^{\frac{5}{2}}} + 8(\frac{\frac{-3}{2}(-4*2X + 0)}{(-4X^{2} + 1)^{\frac{5}{2}}})\\=&\frac{1920X^{3}}{(-4X^{2} + 1)^{\frac{7}{2}}} + \frac{288X}{(-4X^{2} + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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