There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{{(-{x}^{2} + 1)}^{\frac{1}{2}}}{(2x + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(-x^{2} + 1)^{\frac{1}{2}}}{(2x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(-x^{2} + 1)^{\frac{1}{2}}}{(2x + 1)}\right)}{dx}\\=&(\frac{-(2 + 0)}{(2x + 1)^{2}})(-x^{2} + 1)^{\frac{1}{2}} + \frac{(\frac{\frac{1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{1}{2}}})}{(2x + 1)}\\=&\frac{-x}{(2x + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(-x^{2} + 1)^{\frac{1}{2}}}{(2x + 1)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x}{(2x + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(-x^{2} + 1)^{\frac{1}{2}}}{(2x + 1)^{2}}\right)}{dx}\\=&\frac{-(\frac{-(2 + 0)}{(2x + 1)^{2}})x}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x}{(2x + 1)} - \frac{1}{(2x + 1)(-x^{2} + 1)^{\frac{1}{2}}} - 2(\frac{-2(2 + 0)}{(2x + 1)^{3}})(-x^{2} + 1)^{\frac{1}{2}} - \frac{2(\frac{\frac{1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{1}{2}}})}{(2x + 1)^{2}}\\=&\frac{4x}{(2x + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{x^{2}}{(2x + 1)(-x^{2} + 1)^{\frac{3}{2}}} + \frac{8(-x^{2} + 1)^{\frac{1}{2}}}{(2x + 1)^{3}} - \frac{1}{(2x + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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