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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ln({(ln({(ln({(ln(x))}^{4}))}^{3}))}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(ln^{2}(ln^{3}(ln^{4}(x))))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(ln^{2}(ln^{3}(ln^{4}(x))))\right)}{dx}\\=&\frac{2ln(ln^{3}(ln^{4}(x)))*3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{(ln^{2}(ln^{3}(ln^{4}(x))))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)}\\=&\frac{24}{xln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{24}{xln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))}\right)}{dx}\\=&\frac{24*-1}{x^{2}ln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))} + \frac{24*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{xln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)ln(x)ln(ln^{4}(x))} + \frac{24*-1}{xln(ln^{3}(ln^{4}(x)))ln^{2}(x)(x)ln(ln^{4}(x))} + \frac{24*-4ln^{3}(x)}{xln(ln^{3}(ln^{4}(x)))ln(x)ln^{2}(ln^{4}(x))(ln^{4}(x))(x)}\\=&\frac{-24}{x^{2}ln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))} - \frac{288}{x^{2}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{24}{x^{2}ln^{2}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} - \frac{96}{x^{2}ln^{2}(ln^{4}(x))ln^{2}(x)ln(ln^{3}(ln^{4}(x)))}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-24}{x^{2}ln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))} - \frac{288}{x^{2}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{24}{x^{2}ln^{2}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} - \frac{96}{x^{2}ln^{2}(ln^{4}(x))ln^{2}(x)ln(ln^{3}(ln^{4}(x)))}\right)}{dx}\\=&\frac{-24*-2}{x^{3}ln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))} - \frac{24*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{2}ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)ln(x)ln(ln^{4}(x))} - \frac{24*-1}{x^{2}ln(ln^{3}(ln^{4}(x)))ln^{2}(x)(x)ln(ln^{4}(x))} - \frac{24*-4ln^{3}(x)}{x^{2}ln(ln^{3}(ln^{4}(x)))ln(x)ln^{2}(ln^{4}(x))(ln^{4}(x))(x)} - \frac{288*-2}{x^{3}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{288*-2*4ln^{3}(x)}{x^{2}ln^{3}(ln^{4}(x))(ln^{4}(x))(x)ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{288*-2}{x^{2}ln^{2}(ln^{4}(x))ln^{3}(x)(x)ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{288*-2*3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{2}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{3}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)} - \frac{24*-2}{x^{3}ln^{2}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} - \frac{24*-2}{x^{2}ln^{3}(x)(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} - \frac{24*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{2}ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)ln(ln^{4}(x))} - \frac{24*-4ln^{3}(x)}{x^{2}ln^{2}(x)ln(ln^{3}(ln^{4}(x)))ln^{2}(ln^{4}(x))(ln^{4}(x))(x)} - \frac{96*-2}{x^{3}ln^{2}(ln^{4}(x))ln^{2}(x)ln(ln^{3}(ln^{4}(x)))} - \frac{96*-2*4ln^{3}(x)}{x^{2}ln^{3}(ln^{4}(x))(ln^{4}(x))(x)ln^{2}(x)ln(ln^{3}(ln^{4}(x)))} - \frac{96*-2}{x^{2}ln^{2}(ln^{4}(x))ln^{3}(x)(x)ln(ln^{3}(ln^{4}(x)))} - \frac{96*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{2}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)}\\=&\frac{48}{x^{3}ln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))} + \frac{864}{x^{3}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{72}{x^{3}ln^{2}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} + \frac{288}{x^{3}ln^{2}(ln^{4}(x))ln^{2}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{2304}{x^{3}ln^{3}(ln^{4}(x))ln^{3}(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{576}{x^{3}ln^{3}(x)ln^{2}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{6912}{x^{3}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{3}(ln^{3}(ln^{4}(x)))} + \frac{48}{x^{3}ln^{3}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} + \frac{288}{x^{3}ln^{2}(ln^{3}(ln^{4}(x)))ln^{3}(x)ln^{2}(ln^{4}(x))} + \frac{96}{x^{3}ln^{2}(ln^{4}(x))ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{768}{x^{3}ln^{3}(ln^{4}(x))ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{192}{x^{3}ln^{3}(x)ln^{2}(ln^{4}(x))ln(ln^{3}(ln^{4}(x)))} + \frac{1152}{x^{3}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{48}{x^{3}ln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))} + \frac{864}{x^{3}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{72}{x^{3}ln^{2}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} + \frac{288}{x^{3}ln^{2}(ln^{4}(x))ln^{2}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{2304}{x^{3}ln^{3}(ln^{4}(x))ln^{3}(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{576}{x^{3}ln^{3}(x)ln^{2}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{6912}{x^{3}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{3}(ln^{3}(ln^{4}(x)))} + \frac{48}{x^{3}ln^{3}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} + \frac{288}{x^{3}ln^{2}(ln^{3}(ln^{4}(x)))ln^{3}(x)ln^{2}(ln^{4}(x))} + \frac{96}{x^{3}ln^{2}(ln^{4}(x))ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{768}{x^{3}ln^{3}(ln^{4}(x))ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{192}{x^{3}ln^{3}(x)ln^{2}(ln^{4}(x))ln(ln^{3}(ln^{4}(x)))} + \frac{1152}{x^{3}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))}\right)}{dx}\\=&\frac{48*-3}{x^{4}ln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))} + \frac{48*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)ln(x)ln(ln^{4}(x))} + \frac{48*-1}{x^{3}ln(ln^{3}(ln^{4}(x)))ln^{2}(x)(x)ln(ln^{4}(x))} + \frac{48*-4ln^{3}(x)}{x^{3}ln(ln^{3}(ln^{4}(x)))ln(x)ln^{2}(ln^{4}(x))(ln^{4}(x))(x)} + \frac{864*-3}{x^{4}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{864*-2*4ln^{3}(x)}{x^{3}ln^{3}(ln^{4}(x))(ln^{4}(x))(x)ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{864*-2}{x^{3}ln^{2}(ln^{4}(x))ln^{3}(x)(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{864*-2*3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{3}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)} + \frac{72*-3}{x^{4}ln^{2}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} + \frac{72*-2}{x^{3}ln^{3}(x)(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} + \frac{72*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)ln(ln^{4}(x))} + \frac{72*-4ln^{3}(x)}{x^{3}ln^{2}(x)ln(ln^{3}(ln^{4}(x)))ln^{2}(ln^{4}(x))(ln^{4}(x))(x)} + \frac{288*-3}{x^{4}ln^{2}(ln^{4}(x))ln^{2}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{288*-2*4ln^{3}(x)}{x^{3}ln^{3}(ln^{4}(x))(ln^{4}(x))(x)ln^{2}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{288*-2}{x^{3}ln^{2}(ln^{4}(x))ln^{3}(x)(x)ln(ln^{3}(ln^{4}(x)))} + \frac{288*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)} + \frac{2304*-3}{x^{4}ln^{3}(ln^{4}(x))ln^{3}(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{2304*-3*4ln^{3}(x)}{x^{3}ln^{4}(ln^{4}(x))(ln^{4}(x))(x)ln^{3}(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{2304*-3}{x^{3}ln^{3}(ln^{4}(x))ln^{4}(x)(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{2304*-2*3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{3}(ln^{4}(x))ln^{3}(x)ln^{3}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)} + \frac{576*-3}{x^{4}ln^{3}(x)ln^{2}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{576*-3}{x^{3}ln^{4}(x)(x)ln^{2}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{576*-2*4ln^{3}(x)}{x^{3}ln^{3}(x)ln^{3}(ln^{4}(x))(ln^{4}(x))(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{576*-2*3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{3}(x)ln^{2}(ln^{4}(x))ln^{3}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)} + \frac{6912*-3}{x^{4}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{3}(ln^{3}(ln^{4}(x)))} + \frac{6912*-3}{x^{3}ln^{4}(x)(x)ln^{3}(ln^{4}(x))ln^{3}(ln^{3}(ln^{4}(x)))} + \frac{6912*-3*4ln^{3}(x)}{x^{3}ln^{3}(x)ln^{4}(ln^{4}(x))(ln^{4}(x))(x)ln^{3}(ln^{3}(ln^{4}(x)))} + \frac{6912*-3*3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{4}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)} + \frac{48*-3}{x^{4}ln^{3}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} + \frac{48*-3}{x^{3}ln^{4}(x)(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} + \frac{48*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{3}(x)ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)ln(ln^{4}(x))} + \frac{48*-4ln^{3}(x)}{x^{3}ln^{3}(x)ln(ln^{3}(ln^{4}(x)))ln^{2}(ln^{4}(x))(ln^{4}(x))(x)} + \frac{288*-3}{x^{4}ln^{2}(ln^{3}(ln^{4}(x)))ln^{3}(x)ln^{2}(ln^{4}(x))} + \frac{288*-2*3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{3}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)ln^{3}(x)ln^{2}(ln^{4}(x))} + \frac{288*-3}{x^{3}ln^{2}(ln^{3}(ln^{4}(x)))ln^{4}(x)(x)ln^{2}(ln^{4}(x))} + \frac{288*-2*4ln^{3}(x)}{x^{3}ln^{2}(ln^{3}(ln^{4}(x)))ln^{3}(x)ln^{3}(ln^{4}(x))(ln^{4}(x))(x)} + \frac{96*-3}{x^{4}ln^{2}(ln^{4}(x))ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{96*-2*4ln^{3}(x)}{x^{3}ln^{3}(ln^{4}(x))(ln^{4}(x))(x)ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{96*-3}{x^{3}ln^{2}(ln^{4}(x))ln^{4}(x)(x)ln(ln^{3}(ln^{4}(x)))} + \frac{96*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{2}(ln^{4}(x))ln^{3}(x)ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)} + \frac{768*-3}{x^{4}ln^{3}(ln^{4}(x))ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{768*-3*4ln^{3}(x)}{x^{3}ln^{4}(ln^{4}(x))(ln^{4}(x))(x)ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} + \frac{768*-3}{x^{3}ln^{3}(ln^{4}(x))ln^{4}(x)(x)ln(ln^{3}(ln^{4}(x)))} + \frac{768*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{3}(ln^{4}(x))ln^{3}(x)ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)} + \frac{192*-3}{x^{4}ln^{3}(x)ln^{2}(ln^{4}(x))ln(ln^{3}(ln^{4}(x)))} + \frac{192*-3}{x^{3}ln^{4}(x)(x)ln^{2}(ln^{4}(x))ln(ln^{3}(ln^{4}(x)))} + \frac{192*-2*4ln^{3}(x)}{x^{3}ln^{3}(x)ln^{3}(ln^{4}(x))(ln^{4}(x))(x)ln(ln^{3}(ln^{4}(x)))} + \frac{192*-3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{3}(x)ln^{2}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)} + \frac{1152*-3}{x^{4}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{1152*-3}{x^{3}ln^{4}(x)(x)ln^{3}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{1152*-3*4ln^{3}(x)}{x^{3}ln^{3}(x)ln^{4}(ln^{4}(x))(ln^{4}(x))(x)ln^{2}(ln^{3}(ln^{4}(x)))} + \frac{1152*-2*3ln^{2}(ln^{4}(x))*4ln^{3}(x)}{x^{3}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{3}(ln^{3}(ln^{4}(x)))(ln^{3}(ln^{4}(x)))(ln^{4}(x))(x)}\\=&\frac{-144}{x^{4}ln(ln^{3}(ln^{4}(x)))ln(x)ln(ln^{4}(x))} - \frac{3168}{x^{4}ln^{2}(ln^{4}(x))ln^{2}(x)ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{264}{x^{4}ln^{2}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} - \frac{1056}{x^{4}ln^{2}(ln^{4}(x))ln^{2}(x)ln(ln^{3}(ln^{4}(x)))} - \frac{13824}{x^{4}ln^{3}(ln^{4}(x))ln^{3}(x)ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{3456}{x^{4}ln^{3}(x)ln^{2}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{41472}{x^{4}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{3}(ln^{3}(ln^{4}(x)))} - \frac{288}{x^{4}ln^{3}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} - \frac{1728}{x^{4}ln^{2}(ln^{3}(ln^{4}(x)))ln^{3}(x)ln^{2}(ln^{4}(x))} - \frac{576}{x^{4}ln^{2}(ln^{4}(x))ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} - \frac{4608}{x^{4}ln^{3}(ln^{4}(x))ln^{3}(x)ln(ln^{3}(ln^{4}(x)))} - \frac{1152}{x^{4}ln^{3}(x)ln^{2}(ln^{4}(x))ln(ln^{3}(ln^{4}(x)))} - \frac{6912}{x^{4}ln^{3}(x)ln^{3}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{27648}{x^{4}ln^{4}(ln^{4}(x))ln^{4}(x)ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{18432}{x^{4}ln^{4}(x)ln^{3}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{165888}{x^{4}ln^{4}(x)ln^{4}(ln^{4}(x))ln^{3}(ln^{3}(ln^{4}(x)))} - \frac{1728}{x^{4}ln^{4}(x)ln^{2}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{34560}{x^{4}ln^{4}(x)ln^{3}(ln^{4}(x))ln^{3}(ln^{3}(ln^{4}(x)))} - \frac{248832}{x^{4}ln^{4}(x)ln^{4}(ln^{4}(x))ln^{4}(ln^{3}(ln^{4}(x)))} - \frac{144}{x^{4}ln^{4}(x)ln(ln^{3}(ln^{4}(x)))ln(ln^{4}(x))} - \frac{576}{x^{4}ln^{2}(ln^{3}(ln^{4}(x)))ln^{2}(ln^{4}(x))ln^{4}(x)} - \frac{192}{x^{4}ln^{2}(ln^{4}(x))ln^{4}(x)ln(ln^{3}(ln^{4}(x)))} - \frac{6912}{x^{4}ln^{3}(ln^{4}(x))ln^{4}(x)ln^{3}(ln^{3}(ln^{4}(x)))} - \frac{864}{x^{4}ln^{4}(x)ln^{2}(ln^{3}(ln^{4}(x)))ln^{2}(ln^{4}(x))} - \frac{2304}{x^{4}ln^{3}(ln^{4}(x))ln^{4}(x)ln^{2}(ln^{3}(ln^{4}(x)))} - \frac{768}{x^{4}ln^{3}(ln^{4}(x))ln^{4}(x)ln(ln^{3}(ln^{4}(x)))} - \frac{864}{x^{4}ln^{4}(x)ln^{2}(ln^{4}(x))ln(ln^{3}(ln^{4}(x)))} - \frac{9216}{x^{4}ln^{4}(ln^{4}(x))ln^{4}(x)ln(ln^{3}(ln^{4}(x)))} - \frac{3840}{x^{4}ln^{4}(x)ln^{3}(ln^{4}(x))ln(ln^{3}(ln^{4}(x)))} - \frac{23040}{x^{4}ln^{4}(x)ln^{4}(ln^{4}(x))ln^{2}(ln^{3}(ln^{4}(x)))}\\ \end{split}\end{equation} \]