There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(arcsin(x))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arcsin^{2}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin^{2}(x)\right)}{dx}\\=&(\frac{2arcsin(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})\\=&\frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin(x) + \frac{2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin(x) + \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{6x^{2}arcsin(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{2x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{4x}{(-x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6x^{2}arcsin(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{2x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{4x}{(-x^{2} + 1)^{2}}\right)}{dx}\\=&6(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}arcsin(x) + \frac{6*2xarcsin(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{6x^{2}(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} + 2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})arcsin(x) + \frac{2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + 4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x + \frac{4}{(-x^{2} + 1)^{2}}\\=&\frac{30x^{3}arcsin(x)}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{18xarcsin(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{6x^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}} + \frac{24x^{2}}{(-x^{2} + 1)^{3}} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{6}{(-x^{2} + 1)^{2}}\\ \end{split}\end{equation} \]

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