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

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