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 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 2lg(tan(x + X{\frac{1}{x}}^{2}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2lg(tan(x + \frac{X}{x^{2}}))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2lg(tan(x + \frac{X}{x^{2}}))\right)}{dx}\\=&\frac{2sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{ln{10}(tan(x + \frac{X}{x^{2}}))}\\=&\frac{2sec^{2}(x + \frac{X}{x^{2}})}{ln{10}tan(x + \frac{X}{x^{2}})} - \frac{4Xsec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan(x + \frac{X}{x^{2}})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2sec^{2}(x + \frac{X}{x^{2}})}{ln{10}tan(x + \frac{X}{x^{2}})} - \frac{4Xsec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan(x + \frac{X}{x^{2}})}\right)}{dx}\\=&\frac{2*-0sec^{2}(x + \frac{X}{x^{2}})}{ln^{2}{10}tan(x + \frac{X}{x^{2}})} + \frac{2*-sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{2}(x + \frac{X}{x^{2}})}{ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{2*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{ln{10}tan(x + \frac{X}{x^{2}})} - \frac{4X*-3sec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{4X*-0sec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln^{2}{10}tan(x + \frac{X}{x^{2}})} - \frac{4X*-sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{4X*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{3}ln{10}tan(x + \frac{X}{x^{2}})}\\=&\frac{-2sec^{4}(x + \frac{X}{x^{2}})}{ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{8Xsec^{4}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{4sec^{2}(x + \frac{X}{x^{2}})}{ln{10}} - \frac{16Xsec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln{10}} + \frac{12Xsec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{8X^{2}sec^{4}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{16X^{2}sec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2sec^{4}(x + \frac{X}{x^{2}})}{ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{8Xsec^{4}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{4sec^{2}(x + \frac{X}{x^{2}})}{ln{10}} - \frac{16Xsec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln{10}} + \frac{12Xsec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{8X^{2}sec^{4}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{16X^{2}sec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln{10}}\right)}{dx}\\=&\frac{-2*-0sec^{4}(x + \frac{X}{x^{2}})}{ln^{2}{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{2*-2sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{4}(x + \frac{X}{x^{2}})}{ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{2*4sec^{4}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{8X*-3sec^{4}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{8X*-0sec^{4}(x + \frac{X}{x^{2}})}{x^{3}ln^{2}{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{8X*-2sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{4}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{3}(x + \frac{X}{x^{2}})} + \frac{8X*4sec^{4}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{3}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{4*-0sec^{2}(x + \frac{X}{x^{2}})}{ln^{2}{10}} + \frac{4*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{ln{10}} - \frac{16X*-3sec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln{10}} - \frac{16X*-0sec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln^{2}{10}} - \frac{16X*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{3}ln{10}} + \frac{12X*-4sec^{2}(x + \frac{X}{x^{2}})}{x^{5}ln{10}tan(x + \frac{X}{x^{2}})} + \frac{12X*-0sec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln^{2}{10}tan(x + \frac{X}{x^{2}})} + \frac{12X*-sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{12X*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{4}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{8X^{2}*-6sec^{4}(x + \frac{X}{x^{2}})}{x^{7}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{8X^{2}*-0sec^{4}(x + \frac{X}{x^{2}})}{x^{6}ln^{2}{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{8X^{2}*-2sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{4}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{8X^{2}*4sec^{4}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{6}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{16X^{2}*-6sec^{2}(x + \frac{X}{x^{2}})}{x^{7}ln{10}} + \frac{16X^{2}*-0sec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln^{2}{10}} + \frac{16X^{2}*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{6}ln{10}}\\=&\frac{4sec^{6}(x + \frac{X}{x^{2}})}{ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{24Xsec^{6}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{8sec^{4}(x + \frac{X}{x^{2}})}{ln{10}tan(x + \frac{X}{x^{2}})} + \frac{48Xsec^{4}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{36Xsec^{4}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{48X^{2}sec^{6}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{96X^{2}sec^{4}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan(x + \frac{X}{x^{2}})} + \frac{8tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{ln{10}} - \frac{48Xtan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln{10}} + \frac{72Xsec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln{10}} + \frac{72X^{2}sec^{4}(x + \frac{X}{x^{2}})}{x^{7}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{48Xsec^{2}(x + \frac{X}{x^{2}})}{x^{5}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{32X^{3}sec^{6}(x + \frac{X}{x^{2}})}{x^{9}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{144X^{2}sec^{2}(x + \frac{X}{x^{2}})}{x^{7}ln{10}} + \frac{96X^{2}tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln{10}} + \frac{64X^{3}sec^{4}(x + \frac{X}{x^{2}})}{x^{9}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{64X^{3}tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{9}ln{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{4sec^{6}(x + \frac{X}{x^{2}})}{ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{24Xsec^{6}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{8sec^{4}(x + \frac{X}{x^{2}})}{ln{10}tan(x + \frac{X}{x^{2}})} + \frac{48Xsec^{4}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{36Xsec^{4}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{48X^{2}sec^{6}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{96X^{2}sec^{4}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan(x + \frac{X}{x^{2}})} + \frac{8tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{ln{10}} - \frac{48Xtan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln{10}} + \frac{72Xsec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln{10}} + \frac{72X^{2}sec^{4}(x + \frac{X}{x^{2}})}{x^{7}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{48Xsec^{2}(x + \frac{X}{x^{2}})}{x^{5}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{32X^{3}sec^{6}(x + \frac{X}{x^{2}})}{x^{9}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{144X^{2}sec^{2}(x + \frac{X}{x^{2}})}{x^{7}ln{10}} + \frac{96X^{2}tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln{10}} + \frac{64X^{3}sec^{4}(x + \frac{X}{x^{2}})}{x^{9}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{64X^{3}tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{9}ln{10}}\right)}{dx}\\=&\frac{4*-0sec^{6}(x + \frac{X}{x^{2}})}{ln^{2}{10}tan^{3}(x + \frac{X}{x^{2}})} + \frac{4*-3sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{6}(x + \frac{X}{x^{2}})}{ln{10}tan^{4}(x + \frac{X}{x^{2}})} + \frac{4*6sec^{6}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{24X*-3sec^{6}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{24X*-0sec^{6}(x + \frac{X}{x^{2}})}{x^{3}ln^{2}{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{24X*-3sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{6}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{4}(x + \frac{X}{x^{2}})} - \frac{24X*6sec^{6}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{3}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{8*-0sec^{4}(x + \frac{X}{x^{2}})}{ln^{2}{10}tan(x + \frac{X}{x^{2}})} - \frac{8*-sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{4}(x + \frac{X}{x^{2}})}{ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{8*4sec^{4}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{ln{10}tan(x + \frac{X}{x^{2}})} + \frac{48X*-3sec^{4}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan(x + \frac{X}{x^{2}})} + \frac{48X*-0sec^{4}(x + \frac{X}{x^{2}})}{x^{3}ln^{2}{10}tan(x + \frac{X}{x^{2}})} + \frac{48X*-sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{4}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{48X*4sec^{4}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{3}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{36X*-4sec^{4}(x + \frac{X}{x^{2}})}{x^{5}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{36X*-0sec^{4}(x + \frac{X}{x^{2}})}{x^{4}ln^{2}{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{36X*-2sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{4}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{36X*4sec^{4}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{4}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{48X^{2}*-6sec^{6}(x + \frac{X}{x^{2}})}{x^{7}ln{10}tan^{3}(x + \frac{X}{x^{2}})} + \frac{48X^{2}*-0sec^{6}(x + \frac{X}{x^{2}})}{x^{6}ln^{2}{10}tan^{3}(x + \frac{X}{x^{2}})} + \frac{48X^{2}*-3sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{6}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan^{4}(x + \frac{X}{x^{2}})} + \frac{48X^{2}*6sec^{6}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{6}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{96X^{2}*-6sec^{4}(x + \frac{X}{x^{2}})}{x^{7}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{96X^{2}*-0sec^{4}(x + \frac{X}{x^{2}})}{x^{6}ln^{2}{10}tan(x + \frac{X}{x^{2}})} - \frac{96X^{2}*-sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{4}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{96X^{2}*4sec^{4}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{6}ln{10}tan(x + \frac{X}{x^{2}})} + \frac{8*-0tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{ln^{2}{10}} + \frac{8sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{2}(x + \frac{X}{x^{2}})}{ln{10}} + \frac{8tan(x + \frac{X}{x^{2}})*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{ln{10}} - \frac{48X*-3tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln{10}} - \frac{48X*-0tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln^{2}{10}} - \frac{48Xsec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln{10}} - \frac{48Xtan(x + \frac{X}{x^{2}})*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{3}ln{10}} + \frac{72X*-4sec^{2}(x + \frac{X}{x^{2}})}{x^{5}ln{10}} + \frac{72X*-0sec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln^{2}{10}} + \frac{72X*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{4}ln{10}} + \frac{72X^{2}*-7sec^{4}(x + \frac{X}{x^{2}})}{x^{8}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{72X^{2}*-0sec^{4}(x + \frac{X}{x^{2}})}{x^{7}ln^{2}{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{72X^{2}*-2sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{4}(x + \frac{X}{x^{2}})}{x^{7}ln{10}tan^{3}(x + \frac{X}{x^{2}})} + \frac{72X^{2}*4sec^{4}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{7}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{48X*-5sec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{48X*-0sec^{2}(x + \frac{X}{x^{2}})}{x^{5}ln^{2}{10}tan(x + \frac{X}{x^{2}})} - \frac{48X*-sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{2}(x + \frac{X}{x^{2}})}{x^{5}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{48X*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{5}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{32X^{3}*-9sec^{6}(x + \frac{X}{x^{2}})}{x^{10}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{32X^{3}*-0sec^{6}(x + \frac{X}{x^{2}})}{x^{9}ln^{2}{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{32X^{3}*-3sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{6}(x + \frac{X}{x^{2}})}{x^{9}ln{10}tan^{4}(x + \frac{X}{x^{2}})} - \frac{32X^{3}*6sec^{6}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{9}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{144X^{2}*-7sec^{2}(x + \frac{X}{x^{2}})}{x^{8}ln{10}} - \frac{144X^{2}*-0sec^{2}(x + \frac{X}{x^{2}})}{x^{7}ln^{2}{10}} - \frac{144X^{2}*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{7}ln{10}} + \frac{96X^{2}*-6tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{7}ln{10}} + \frac{96X^{2}*-0tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln^{2}{10}} + \frac{96X^{2}sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln{10}} + \frac{96X^{2}tan(x + \frac{X}{x^{2}})*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{6}ln{10}} + \frac{64X^{3}*-9sec^{4}(x + \frac{X}{x^{2}})}{x^{10}ln{10}tan(x + \frac{X}{x^{2}})} + \frac{64X^{3}*-0sec^{4}(x + \frac{X}{x^{2}})}{x^{9}ln^{2}{10}tan(x + \frac{X}{x^{2}})} + \frac{64X^{3}*-sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{4}(x + \frac{X}{x^{2}})}{x^{9}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{64X^{3}*4sec^{4}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{9}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{64X^{3}*-9tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{10}ln{10}} - \frac{64X^{3}*-0tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{9}ln^{2}{10}} - \frac{64X^{3}sec^{2}(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})sec^{2}(x + \frac{X}{x^{2}})}{x^{9}ln{10}} - \frac{64X^{3}tan(x + \frac{X}{x^{2}})*2sec^{2}(x + \frac{X}{x^{2}})tan(x + \frac{X}{x^{2}})(1 + \frac{X*-2}{x^{3}})}{x^{9}ln{10}}\\=&\frac{-12sec^{8}(x + \frac{X}{x^{2}})}{ln{10}tan^{4}(x + \frac{X}{x^{2}})} + \frac{96Xsec^{8}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{4}(x + \frac{X}{x^{2}})} + \frac{32sec^{6}(x + \frac{X}{x^{2}})}{ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{256Xsec^{6}(x + \frac{X}{x^{2}})}{x^{3}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{144Xsec^{6}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{288X^{2}sec^{8}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan^{4}(x + \frac{X}{x^{2}})} + \frac{768X^{2}sec^{6}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{24sec^{4}(x + \frac{X}{x^{2}})}{ln{10}} + \frac{192Xsec^{4}(x + \frac{X}{x^{2}})}{x^{3}ln{10}} - \frac{288Xsec^{4}(x + \frac{X}{x^{2}})}{x^{4}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{576X^{2}sec^{4}(x + \frac{X}{x^{2}})}{x^{6}ln{10}} + \frac{192Xsec^{4}(x + \frac{X}{x^{2}})}{x^{5}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{576X^{2}sec^{6}(x + \frac{X}{x^{2}})}{x^{7}ln{10}tan^{3}(x + \frac{X}{x^{2}})} + \frac{1152X^{2}sec^{4}(x + \frac{X}{x^{2}})}{x^{7}ln{10}tan(x + \frac{X}{x^{2}})} + \frac{384X^{3}sec^{8}(x + \frac{X}{x^{2}})}{x^{9}ln{10}tan^{4}(x + \frac{X}{x^{2}})} - \frac{1024X^{3}sec^{6}(x + \frac{X}{x^{2}})}{x^{9}ln{10}tan^{2}(x + \frac{X}{x^{2}})} + \frac{768X^{3}sec^{4}(x + \frac{X}{x^{2}})}{x^{9}ln{10}} + \frac{16tan^{2}(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{ln{10}} - \frac{128Xtan^{2}(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{3}ln{10}} + \frac{288Xtan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{4}ln{10}} + \frac{384X^{2}tan^{2}(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln{10}} + \frac{576X^{3}sec^{6}(x + \frac{X}{x^{2}})}{x^{10}ln{10}tan^{3}(x + \frac{X}{x^{2}})} - \frac{600X^{2}sec^{4}(x + \frac{X}{x^{2}})}{x^{8}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{1152X^{3}sec^{4}(x + \frac{X}{x^{2}})}{x^{10}ln{10}tan(x + \frac{X}{x^{2}})} + \frac{240Xsec^{2}(x + \frac{X}{x^{2}})}{x^{6}ln{10}tan(x + \frac{X}{x^{2}})} - \frac{192X^{4}sec^{8}(x + \frac{X}{x^{2}})}{x^{12}ln{10}tan^{4}(x + \frac{X}{x^{2}})} - \frac{384Xsec^{2}(x + \frac{X}{x^{2}})}{x^{5}ln{10}} + \frac{1200X^{2}sec^{2}(x + \frac{X}{x^{2}})}{x^{8}ln{10}} + \frac{512X^{4}sec^{6}(x + \frac{X}{x^{2}})}{x^{12}ln{10}tan^{2}(x + \frac{X}{x^{2}})} - \frac{1152X^{2}tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{7}ln{10}} + \frac{1152X^{3}tan(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{10}ln{10}} - \frac{512X^{3}tan^{2}(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{9}ln{10}} - \frac{384X^{4}sec^{4}(x + \frac{X}{x^{2}})}{x^{12}ln{10}} + \frac{256X^{4}tan^{2}(x + \frac{X}{x^{2}})sec^{2}(x + \frac{X}{x^{2}})}{x^{12}ln{10}}\\ \end{split}\end{equation} \]