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

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