Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sqrt(1 + \frac{0.69675{x}^{2}}{({x}^{2} - {0.069066}^{2})} + \frac{0.408218{x}^{2}}{({x}^{2} - {0.115662}^{2})} + \frac{0.890815{x}^{2}}{({x}^{2} - {9.900559}^{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)\right)}{dx}\\=&\frac{(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)*0.5}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}}\\=&\frac{-0.348375x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.4454075}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.4454075}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})x}{(x - 0.115662)(x - 0.115662)} - \frac{0.204109}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})x}{(x - 9.900559)(x - 9.900559)} - \frac{0.4454075}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109(\frac{-(1 + 0)}{(x - 0.115662)^{2}})}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})}{(x - 0.115662)} + \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})}{(x - 0.069066)} + \frac{0.4454075(\frac{-(1 + 0)}{(x - 9.900559)^{2}})}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.4454075(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})}{(x - 9.900559)}\\=&\frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.121365140625x^{2}}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} - \frac{0.071106472875x^{2}}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} - \frac{0.1551688378125x^{2}}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.071106472875x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} + \frac{0.121365140625x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} + \frac{0.1551688378125x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} + \frac{0.204109x}{(x - 0.115662)(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109x}{(x - 0.115662)(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.071106472875x^{2}}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} - \frac{0.041660483881x^{2}}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} - \frac{0.0909116794175x^{2}}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.041660483881x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} + \frac{0.071106472875x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} + \frac{0.0909116794175x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} + \frac{0.4454075x}{(x - 9.900559)(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.4454075x}{(x - 9.900559)(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.1551688378125x^{2}}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} - \frac{0.0909116794175x^{2}}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} - \frac{0.19838784105625x^{2}}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.0909116794175x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} + \frac{0.1551688378125x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} + \frac{0.19838784105625x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} + \frac{0.071106472875x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} + \frac{0.041660483881x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} + \frac{0.0909116794175x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.121365140625x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} + \frac{0.071106472875x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} + \frac{0.1551688378125x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.1551688378125x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} + \frac{0.0909116794175x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} + \frac{0.19838784105625x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} - \frac{0.204109}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.071106472875}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} - \frac{0.121365140625}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} - \frac{0.1551688378125}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} - \frac{0.041660483881}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} - \frac{0.071106472875}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} - \frac{0.0909116794175}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} - \frac{0.0909116794175}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} - \frac{0.1551688378125}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} - \frac{0.19838784105625}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} - \frac{0.204109}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sqrt(1 + \frac{0.69675{x}^{2}}{({x}^{2} - {0.069066}^{2})} + \frac{0.408218{x}^{2}}{({x}^{2} - {0.115662}^{2})} + \frac{0.890815{x}^{2}}{({x}^{2} - {9.900559}^{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)\right)}{dx}\\=&\frac{(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)*0.5}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}}\\=&\frac{-0.348375x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.4454075}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.4454075}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.204109(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})x}{(x - 0.115662)(x - 0.115662)} - \frac{0.204109}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})x}{(x - 9.900559)(x - 9.900559)} - \frac{0.4454075}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109(\frac{-(1 + 0)}{(x - 0.115662)^{2}})}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})}{(x - 0.115662)} + \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 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)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})}{(x - 0.069066)} + \frac{0.4454075(\frac{-(1 + 0)}{(x - 9.900559)^{2}})}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.4454075(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0.408218(\frac{-(1 + 0)}{(x - 0.115662)^{2}})x + \frac{0.408218}{(x - 0.115662)} + 0.890815(\frac{-(1 + 0)}{(x - 9.900559)^{2}})x + \frac{0.890815}{(x - 9.900559)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}})}{(x - 9.900559)}\\=&\frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.121365140625x^{2}}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} - \frac{0.071106472875x^{2}}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} - \frac{0.1551688378125x^{2}}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.071106472875x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} + \frac{0.121365140625x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} + \frac{0.1551688378125x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} + \frac{0.204109x}{(x - 0.115662)(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.204109x}{(x - 0.115662)(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.071106472875x^{2}}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} - \frac{0.041660483881x^{2}}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} - \frac{0.0909116794175x^{2}}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.041660483881x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} + \frac{0.071106472875x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} + \frac{0.0909116794175x}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} + \frac{0.4454075x}{(x - 9.900559)(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} + \frac{0.4454075x}{(x - 9.900559)(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.1551688378125x^{2}}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} - \frac{0.0909116794175x^{2}}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} - \frac{0.19838784105625x^{2}}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.0909116794175x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} + \frac{0.1551688378125x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} + \frac{0.19838784105625x}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} + \frac{0.071106472875x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} + \frac{0.041660483881x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} + \frac{0.0909116794175x}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.121365140625x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} + \frac{0.071106472875x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} + \frac{0.1551688378125x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} + \frac{0.1551688378125x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} + \frac{0.0909116794175x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)(x - 0.115662)} + \frac{0.19838784105625x}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)(x - 9.900559)} - \frac{0.204109}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.071106472875}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} - \frac{0.121365140625}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} - \frac{0.1551688378125}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} - \frac{0.041660483881}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} - \frac{0.071106472875}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} - \frac{0.0909116794175}{(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} - \frac{0.0909116794175}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.115662)} - \frac{0.1551688378125}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 0.069066)} - \frac{0.19838784105625}{(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{3}{2}}(x - 9.900559)} - \frac{0.204109}{(x - 0.115662)(x - 0.115662)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.4454075}{(x - 9.900559)(x - 9.900559)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + \frac{0.408218x}{(x - 0.115662)} + \frac{0.890815x}{(x - 9.900559)} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]