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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 34.42πx - 0.558arcsin(0.41316πx + \frac{π}{7})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 34.42πx - 0.558arcsin(0.41316πx + 0.142857142857143π)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 34.42πx - 0.558arcsin(0.41316πx + 0.142857142857143π)\right)}{dx}\\=&34.42π - 0.558(\frac{(0.41316π + 0)}{((1 - (0.41316πx + 0.142857142857143π)^{2})^{\frac{1}{2}})})\\=&34.42π - \frac{0.23054328π}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 34.42π - \frac{0.23054328π}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&0 - 0.23054328(\frac{-0.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}})π + 0\\=& - \frac{0.0393540112281128π^{3}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.00680366154034286π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.00680366154034286π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{0.0393540112281128π^{3}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.00680366154034286π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.00680366154034286π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=& - 0.0393540112281128(\frac{-1.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}})π^{3}x - \frac{0.0393540112281128π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - 0.00680366154034286(\frac{-1.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}})π^{3} + 0 - 0.00680366154034286(\frac{-1.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}})π^{3} + 0\\=& - \frac{0.0201533291242637π^{5}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0393540112281128π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{0.0201533291242637π^{5}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0393540112281128π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}}\right)}{dx}\\=& - 0.0201533291242637(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x^{2} - \frac{0.0201533291242637π^{5}*2x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.00348417927407294(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.00348417927407294(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.00348417927407295(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x - \frac{0.00348417927407295π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.00348417927407295(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x - \frac{0.00348417927407295π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.000602357314716012(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5} + 0 - 0.000602357314716012(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5} + 0 - 0.0393540112281128(\frac{-1.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}})π^{3} + 0 - 0.000602357314716012(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5} + 0 - 0.000602357314716012(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5} + 0\\=& - \frac{0.0172009858764941π^{7}x^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0403066582485274π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0201533291242637π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.00348417927407295π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 34.42πx - 0.558arcsin(0.41316πx + \frac{π}{7})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 34.42πx - 0.558arcsin(0.41316πx + 0.142857142857143π)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 34.42πx - 0.558arcsin(0.41316πx + 0.142857142857143π)\right)}{dx}\\=&34.42π - 0.558(\frac{(0.41316π + 0)}{((1 - (0.41316πx + 0.142857142857143π)^{2})^{\frac{1}{2}})})\\=&34.42π - \frac{0.23054328π}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 34.42π - \frac{0.23054328π}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&0 - 0.23054328(\frac{-0.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}})π + 0\\=& - \frac{0.0393540112281128π^{3}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.00680366154034286π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.00680366154034286π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{0.0393540112281128π^{3}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.00680366154034286π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.00680366154034286π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=& - 0.0393540112281128(\frac{-1.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}})π^{3}x - \frac{0.0393540112281128π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - 0.00680366154034286(\frac{-1.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}})π^{3} + 0 - 0.00680366154034286(\frac{-1.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}})π^{3} + 0\\=& - \frac{0.0201533291242637π^{5}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0393540112281128π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{0.0201533291242637π^{5}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0393540112281128π^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{3}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000602357314716012π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}}\right)}{dx}\\=& - 0.0201533291242637(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x^{2} - \frac{0.0201533291242637π^{5}*2x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.00348417927407294(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.00348417927407294(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.00348417927407295(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x - \frac{0.00348417927407295π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.00348417927407295(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5}x - \frac{0.00348417927407295π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - 0.000602357314716012(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5} + 0 - 0.000602357314716012(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5} + 0 - 0.0393540112281128(\frac{-1.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}})π^{3} + 0 - 0.000602357314716012(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5} + 0 - 0.000602357314716012(\frac{-2.5(-0.1707011856π^{2}*2x - 0.0590228571428571π^{2} - 0.0590228571428571π^{2} + 0 + 0)}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}})π^{5} + 0\\=& - \frac{0.0172009858764941π^{7}x^{3}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0403066582485274π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.002973767664636π^{7}x^{2}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0201533291242637π^{5}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.000514115538884278π^{7}x}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.00348417927407295π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.00348417927407295π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.00348417927407294π^{5}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{5}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}} - \frac{0.0000888821243385955π^{7}}{(-0.1707011856π^{2}x^{2} - 0.0590228571428571π^{2}x - 0.0590228571428571π^{2}x - 0.0204081632653061π^{2} + 1)^{\frac{7}{2}}}\\ \end{split}\end{equation} \]