There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sqrt(1 + \frac{0.69675{x}^{2}}{({x}^{2} - {0.069066}^{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{0.69675x}{(x - 0.069066)} + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{0.69675x}{(x - 0.069066)} + 1)\right)}{dx}\\=&\frac{(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0)*0.5}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\\=&\frac{-0.348375x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-0.348375x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{-0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.348375(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}})x}{(x - 0.069066)(x - 0.069066)} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}})}{(x - 0.069066)}\\=&\frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.121365140625x^{2}}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} + \frac{0.121365140625x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)} + \frac{0.121365140625x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.121365140625}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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