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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sqrt(6368.04 - {(\frac{(25637.017706 + 10154.2cos(5.13126x))}{sqrt(36129.9937 + 24740.814cos(5.13126x))} - 133.167)}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)\right)}{dx}\\=&\frac{(\frac{-25637.017706*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{10154.2*-sin(5.13126x)*5.13126}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + 0)*0.5}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\\=& - \frac{322272855.337519sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{26051.920146sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{813664778.953651sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{322272855.337519sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{26051.920146sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{813664778.953651sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\right)}{dx}\\=& - \frac{322272855.337519(\frac{-(24740.814*-sin(5.13126x)*5.13126 + 0)}{(24740.814cos(5.13126x) + 36129.9937)^{2}})sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{322272855.337519(\frac{-0.5(24740.814*-sin(5.13126x)*5.13126 + 0)}{(24740.814cos(5.13126x) + 36129.9937)^{\frac{3}{2}}})sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{322272855.337519(\frac{-0.5(\frac{-25637.017706*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{10154.2*-sin(5.13126x)*5.13126}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + 0)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}})sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{322272855.337519cos(5.13126x)*5.13126cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{322272855.337519sin(5.13126x)*-sin(5.13126x)*5.13126}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{26051.920146(\frac{-0.5(\frac{-25637.017706*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{10154.2*-sin(5.13126x)*5.13126}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + 0)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}})sin(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{26051.920146cos(5.13126x)*5.13126}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{26051.920146sin(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{813664778.953651(\frac{-(24740.814*-sin(5.13126x)*5.13126 + 0)}{(24740.814cos(5.13126x) + 36129.9937)^{2}})sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{813664778.953651(\frac{-0.5(24740.814*-sin(5.13126x)*5.13126 + 0)}{(24740.814cos(5.13126x) + 36129.9937)^{\frac{3}{2}}})sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{813664778.953651(\frac{-0.5(\frac{-25637.017706*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{10154.2*-sin(5.13126x)*5.13126}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + 0)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}})sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{813664778.953651cos(5.13126x)*5.13126}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\\=& - \frac{40913038264914.1sin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{8395826692476.47sin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{%.0-3lfsin(5.13126x)sin(5.13126x)cos(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + \frac{8395826692476.47sin(5.13126x)sin(5.13126x)cos(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{%.0-3lfsin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{1653665811.6792cos(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{20456519132457.1sin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{3}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{21197529846913.3sin(5.13126x)sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{678702543.293561sin(5.13126x)sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{21197529846913.3sin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{133679.175768364cos(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{1653665811.6792sin(5.13126x)sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{103296004254777sin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{51648002127388.6sin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{3}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{%.0-3lfsin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + \frac{1653665811.6792sin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{%.0-3lfsin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{4175125533.65371cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sqrt(6368.04 - {(\frac{(25637.017706 + 10154.2cos(5.13126x))}{sqrt(36129.9937 + 24740.814cos(5.13126x))} - 133.167)}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)\right)}{dx}\\=&\frac{(\frac{-25637.017706*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{10154.2*-sin(5.13126x)*5.13126}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + 0)*0.5}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\\=& - \frac{322272855.337519sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{26051.920146sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{813664778.953651sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{322272855.337519sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{26051.920146sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{813664778.953651sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\right)}{dx}\\=& - \frac{322272855.337519(\frac{-(24740.814*-sin(5.13126x)*5.13126 + 0)}{(24740.814cos(5.13126x) + 36129.9937)^{2}})sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{322272855.337519(\frac{-0.5(24740.814*-sin(5.13126x)*5.13126 + 0)}{(24740.814cos(5.13126x) + 36129.9937)^{\frac{3}{2}}})sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{322272855.337519(\frac{-0.5(\frac{-25637.017706*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{10154.2*-sin(5.13126x)*5.13126}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + 0)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}})sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{322272855.337519cos(5.13126x)*5.13126cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{322272855.337519sin(5.13126x)*-sin(5.13126x)*5.13126}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{26051.920146(\frac{-0.5(\frac{-25637.017706*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{10154.2*-sin(5.13126x)*5.13126}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + 0)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}})sin(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{26051.920146cos(5.13126x)*5.13126}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{26051.920146sin(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{813664778.953651(\frac{-(24740.814*-sin(5.13126x)*5.13126 + 0)}{(24740.814cos(5.13126x) + 36129.9937)^{2}})sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{813664778.953651(\frac{-0.5(24740.814*-sin(5.13126x)*5.13126 + 0)}{(24740.814cos(5.13126x) + 36129.9937)^{\frac{3}{2}}})sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{813664778.953651(\frac{-0.5(\frac{-25637.017706*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{10154.2*-sin(5.13126x)*5.13126}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)*-(24740.814*-sin(5.13126x)*5.13126 + 0)*0.5}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + 0)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}})sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{813664778.953651cos(5.13126x)*5.13126}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\\=& - \frac{40913038264914.1sin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{8395826692476.47sin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{%.0-3lfsin(5.13126x)sin(5.13126x)cos(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + \frac{8395826692476.47sin(5.13126x)sin(5.13126x)cos(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{%.0-3lfsin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{1653665811.6792cos(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{20456519132457.1sin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{3}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} + \frac{21197529846913.3sin(5.13126x)sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{678702543.293561sin(5.13126x)sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{21197529846913.3sin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{133679.175768364cos(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}sqrt(24740.814cos(5.13126x) + 36129.9937)} + \frac{1653665811.6792sin(5.13126x)sin(5.13126x)}{(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{103296004254777sin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{51648002127388.6sin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{3}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{%.0-3lfsin(5.13126x)sin(5.13126x)cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} + \frac{1653665811.6792sin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}} - \frac{%.0-3lfsin(5.13126x)sin(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{3}{2}}(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}} - \frac{4175125533.65371cos(5.13126x)}{(24740.814cos(5.13126x) + 36129.9937)(24740.814cos(5.13126x) + 36129.9937)^{\frac{1}{2}}(\frac{-25637.017706}{sqrt(24740.814cos(5.13126x) + 36129.9937)} - \frac{10154.2cos(5.13126x)}{sqrt(24740.814cos(5.13126x) + 36129.9937)} + 6501.207)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]