There are 1 questions in this calculation: for each question, the 4 derivative of o is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ arcsin_{o}^{e^{o}}\ with\ respect\ to\ o：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin_{o}^{e^{o}}\right)}{do}\\=&(\frac{(1)}{((1 - (o)^{2})^{\frac{1}{2}})})\\=&\frac{1}{(-o^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{(-o^{2} + 1)^{\frac{1}{2}}}\right)}{do}\\=&(\frac{\frac{-1}{2}(-2o + 0)}{(-o^{2} + 1)^{\frac{3}{2}}})\\=&\frac{o}{(-o^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{o}{(-o^{2} + 1)^{\frac{3}{2}}}\right)}{do}\\=&(\frac{\frac{-3}{2}(-2o + 0)}{(-o^{2} + 1)^{\frac{5}{2}}})o + \frac{1}{(-o^{2} + 1)^{\frac{3}{2}}}\\=&\frac{3o^{2}}{(-o^{2} + 1)^{\frac{5}{2}}} + \frac{1}{(-o^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3o^{2}}{(-o^{2} + 1)^{\frac{5}{2}}} + \frac{1}{(-o^{2} + 1)^{\frac{3}{2}}}\right)}{do}\\=&3(\frac{\frac{-5}{2}(-2o + 0)}{(-o^{2} + 1)^{\frac{7}{2}}})o^{2} + \frac{3*2o}{(-o^{2} + 1)^{\frac{5}{2}}} + (\frac{\frac{-3}{2}(-2o + 0)}{(-o^{2} + 1)^{\frac{5}{2}}})\\=&\frac{15o^{3}}{(-o^{2} + 1)^{\frac{7}{2}}} + \frac{9o}{(-o^{2} + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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