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

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