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 12 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 12th\ derivative\ of\ function\ {x}^{(1 - ln(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {x}^{(-ln(x) + 1)}\\\\ &\color{blue}{The\ 12th\ derivative\ of\ function:} \\=&\frac{93651048{x}^{(-ln(x) + 1)}ln^{2}(x)ln(x)}{x^{12}} + \frac{30483728{x}^{(-ln(x) + 1)}ln^{3}(x)ln(x)}{x^{12}} + \frac{45404238{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{2}(x)}{x^{12}} - \frac{14510880{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{3}(x)}{x^{12}} + \frac{18053628{x}^{(-ln(x) + 1)}ln(x)ln(x)}{x^{12}} - \frac{16374420{x}^{(-ln(x) + 1)}ln^{4}(x)ln(x)}{x^{12}} - \frac{23629860{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{2}(x)}{x^{12}} - \frac{22270930{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{3}(x)}{x^{12}} + \frac{74182464{x}^{(-ln(x) + 1)}ln(x)ln^{2}(x)}{x^{12}} + \frac{74182464{x}^{(-ln(x) + 1)}ln(x)ln^{2}(x)}{x^{12}} - \frac{23629860{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{2}(x)}{x^{12}} + \frac{93651048{x}^{(-ln(x) + 1)}ln^{2}(x)ln(x)}{x^{12}} - \frac{12973070{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{4}(x)}{x^{12}} + \frac{30055256{x}^{(-ln(x) + 1)}ln(x)ln^{3}(x)}{x^{12}} + \frac{45404238{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{2}(x)}{x^{12}} - \frac{20433325{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{2}(x)}{x^{12}} - \frac{20433325{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{2}(x)}{x^{12}} - \frac{4593960{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{3}(x)}{x^{12}} + \frac{30483728{x}^{(-ln(x) + 1)}ln^{3}(x)ln(x)}{x^{12}} + \frac{30055256{x}^{(-ln(x) + 1)}ln(x)ln^{3}(x)}{x^{12}} - \frac{14510880{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{3}(x)}{x^{12}} - \frac{9665381{x}^{(-ln(x) + 1)}ln^{5}(x)ln(x)}{x^{12}} + \frac{18053628{x}^{(-ln(x) + 1)}ln(x)ln(x)}{x^{12}} - \frac{22270930{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{3}(x)}{x^{12}} - \frac{4283370{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{4}(x)}{x^{12}} - \frac{4593960{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{3}(x)}{x^{12}} - \frac{2695950{x}^{(-ln(x) + 1)}ln(x)ln^{4}(x)}{x^{12}} - \frac{2942730{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{2}(x)}{x^{12}} + \frac{1255485{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{3}(x)}{x^{12}} - \frac{16374420{x}^{(-ln(x) + 1)}ln^{4}(x)ln(x)}{x^{12}} - \frac{2695950{x}^{(-ln(x) + 1)}ln(x)ln^{4}(x)}{x^{12}} - \frac{2383668{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{5}(x)}{x^{12}} - \frac{12973070{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{4}(x)}{x^{12}} - \frac{2942730{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{2}(x)}{x^{12}} + \frac{1109955{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{4}(x)}{x^{12}} + \frac{811503{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{2}(x)}{x^{12}} + \frac{624960{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{3}(x)}{x^{12}} - \frac{9665381{x}^{(-ln(x) + 1)}ln^{5}(x)ln(x)}{x^{12}} + \frac{520443{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{5}(x)}{x^{12}} - \frac{4283370{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{4}(x)}{x^{12}} + \frac{1109955{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{4}(x)}{x^{12}} + \frac{769860{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{4}(x)}{x^{12}} + \frac{315720{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{2}(x)}{x^{12}} - \frac{3697177{x}^{(-ln(x) + 1)}ln(x)ln^{5}(x)}{x^{12}} + \frac{95700{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{3}(x)}{x^{12}} - \frac{1043028{x}^{(-ln(x) + 1)}ln^{6}(x)ln(x)}{x^{12}} + \frac{602280{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{5}(x)}{x^{12}} + \frac{143220{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{4}(x)}{x^{12}} - \frac{2383668{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{5}(x)}{x^{12}} - \frac{1043028{x}^{(-ln(x) + 1)}ln^{6}(x)ln(x)}{x^{12}} + \frac{41085{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{2}(x)}{x^{12}} + \frac{6480{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{3}(x)}{x^{12}} + \frac{284361{x}^{(-ln(x) + 1)}ln^{7}(x)ln(x)}{x^{12}} + \frac{142758{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{5}(x)}{x^{12}} + \frac{11340{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{4}(x)}{x^{12}} - \frac{3697177{x}^{(-ln(x) + 1)}ln(x)ln^{5}(x)}{x^{12}} + \frac{1255485{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{3}(x)}{x^{12}} + \frac{76461{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{6}(x)}{x^{12}} + \frac{2430{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{2}(x)}{x^{12}} + \frac{165{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{3}(x)}{x^{12}} + \frac{90900{x}^{(-ln(x) + 1)}ln^{8}(x)ln(x)}{x^{12}} + \frac{13608{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{5}(x)}{x^{12}} + \frac{520443{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{5}(x)}{x^{12}} + \frac{330{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{4}(x)}{x^{12}} + \frac{602280{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{5}(x)}{x^{12}} + \frac{289800{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{6}(x)}{x^{12}} - \frac{732438{x}^{(-ln(x) + 1)}ln(x)ln^{6}(x)}{x^{12}} + \frac{55{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{2}(x)}{x^{12}} + \frac{11{x}^{(-ln(x) + 1)}ln^{11}(x)ln(x)}{x^{12}} + \frac{76461{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{6}(x)}{x^{12}} + \frac{10285{x}^{(-ln(x) + 1)}ln^{9}(x)ln(x)}{x^{12}} + \frac{540{x}^{(-ln(x) + 1)}ln^{10}(x)ln(x)}{x^{12}} + \frac{811503{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{2}(x)}{x^{12}} + \frac{462{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{5}(x)}{x^{12}} + \frac{94710{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{6}(x)}{x^{12}} + \frac{462{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{6}(x)}{x^{12}} + \frac{769860{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{4}(x)}{x^{12}} + \frac{11340{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{6}(x)}{x^{12}} + \frac{289800{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{6}(x)}{x^{12}} + \frac{330{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{7}(x)}{x^{12}} - \frac{30657{x}^{(-ln(x) + 1)}ln(x)ln^{7}(x)}{x^{12}} + \frac{94710{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{6}(x)}{x^{12}} + \frac{6480{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{7}(x)}{x^{12}} + \frac{76320{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{7}(x)}{x^{12}} + \frac{165{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{8}(x)}{x^{12}} + \frac{624960{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{3}(x)}{x^{12}} + \frac{40260{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{7}(x)}{x^{12}} + \frac{142758{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{5}(x)}{x^{12}} + \frac{2430{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{8}(x)}{x^{12}} + \frac{7110{x}^{(-ln(x) + 1)}ln(x)ln^{8}(x)}{x^{12}} + \frac{40260{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{7}(x)}{x^{12}} + \frac{55{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{9}(x)}{x^{12}} + \frac{9900{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{8}(x)}{x^{12}} + \frac{6480{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{7}(x)}{x^{12}} + \frac{76320{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{7}(x)}{x^{12}} + \frac{143220{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{4}(x)}{x^{12}} + \frac{11340{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{6}(x)}{x^{12}} + \frac{9900{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{8}(x)}{x^{12}} + \frac{284361{x}^{(-ln(x) + 1)}ln^{7}(x)ln(x)}{x^{12}} - \frac{732438{x}^{(-ln(x) + 1)}ln(x)ln^{6}(x)}{x^{12}} + \frac{2430{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{8}(x)}{x^{12}} + \frac{1045{x}^{(-ln(x) + 1)}ln(x)ln^{9}(x)}{x^{12}} + \frac{165{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{8}(x)}{x^{12}} + \frac{540{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{9}(x)}{x^{12}} + \frac{13608{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{5}(x)}{x^{12}} + \frac{11{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{10}(x)}{x^{12}} + \frac{330{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{7}(x)}{x^{12}} + \frac{315720{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{2}(x)}{x^{12}} + \frac{55{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{9}(x)}{x^{12}} + \frac{11{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{10}(x)}{x^{12}} + \frac{540{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{9}(x)}{x^{12}} + \frac{95700{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{3}(x)}{x^{12}} - \frac{30657{x}^{(-ln(x) + 1)}ln(x)ln^{7}(x)}{x^{12}} + \frac{462{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{6}(x)}{x^{12}} + \frac{7110{x}^{(-ln(x) + 1)}ln(x)ln^{8}(x)}{x^{12}} + \frac{462{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{5}(x)}{x^{12}} + \frac{1045{x}^{(-ln(x) + 1)}ln(x)ln^{9}(x)}{x^{12}} + \frac{41085{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{2}(x)}{x^{12}} + \frac{11340{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{4}(x)}{x^{12}} + \frac{330{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{4}(x)}{x^{12}} + \frac{6480{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{3}(x)}{x^{12}} + \frac{90900{x}^{(-ln(x) + 1)}ln^{8}(x)ln(x)}{x^{12}} + \frac{165{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{3}(x)}{x^{12}} + \frac{10285{x}^{(-ln(x) + 1)}ln^{9}(x)ln(x)}{x^{12}} + \frac{2430{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{2}(x)}{x^{12}} + \frac{540{x}^{(-ln(x) + 1)}ln^{10}(x)ln(x)}{x^{12}} + \frac{54{x}^{(-ln(x) + 1)}ln(x)ln^{10}(x)}{x^{12}} + \frac{54{x}^{(-ln(x) + 1)}ln(x)ln^{10}(x)}{x^{12}} + \frac{55{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{2}(x)}{x^{12}} + \frac{11{x}^{(-ln(x) + 1)}ln^{11}(x)ln(x)}{x^{12}} + \frac{{x}^{(-ln(x) + 1)}ln(x)ln^{11}(x)}{x^{12}} + \frac{{x}^{(-ln(x) + 1)}ln(x)ln^{11}(x)}{x^{12}} - \frac{2227093{x}^{(-ln(x) + 1)}ln^{6}(x)}{x^{12}} + \frac{18053628{x}^{(-ln(x) + 1)}ln^{2}(x)}{x^{12}} - \frac{253638{x}^{(-ln(x) + 1)}ln^{7}(x)}{x^{12}} + \frac{55944504{x}^{(-ln(x) + 1)}ln^{3}(x)}{x^{12}} + \frac{18053628{x}^{(-ln(x) + 1)}ln^{2}(x)}{x^{12}} + \frac{31713{x}^{(-ln(x) + 1)}ln^{8}(x)}{x^{12}} - \frac{3814074{x}^{(-ln(x) + 1)}ln^{5}(x)}{x^{12}} + \frac{1133{x}^{(-ln(x) + 1)}ln^{10}(x)}{x^{12}} + \frac{15134746{x}^{(-ln(x) + 1)}ln^{4}(x)}{x^{12}} + \frac{31713{x}^{(-ln(x) + 1)}ln^{8}(x)}{x^{12}} + \frac{10890{x}^{(-ln(x) + 1)}ln^{9}(x)}{x^{12}} + \frac{10890{x}^{(-ln(x) + 1)}ln^{9}(x)}{x^{12}} - \frac{253638{x}^{(-ln(x) + 1)}ln^{7}(x)}{x^{12}} + \frac{15134746{x}^{(-ln(x) + 1)}ln^{4}(x)}{x^{12}} + \frac{55944504{x}^{(-ln(x) + 1)}ln^{3}(x)}{x^{12}} + \frac{1133{x}^{(-ln(x) + 1)}ln^{10}(x)}{x^{12}} - \frac{2227093{x}^{(-ln(x) + 1)}ln^{6}(x)}{x^{12}} - \frac{3814074{x}^{(-ln(x) + 1)}ln^{5}(x)}{x^{12}} + \frac{54{x}^{(-ln(x) + 1)}ln^{11}(x)}{x^{12}} + \frac{{x}^{(-ln(x) + 1)}ln^{12}(x)}{x^{12}} - \frac{80014824{x}^{(-ln(x) + 1)}ln(x)}{x^{12}} + \frac{54{x}^{(-ln(x) + 1)}ln^{11}(x)}{x^{12}} - \frac{80014824{x}^{(-ln(x) + 1)}ln(x)}{x^{12}} + \frac{{x}^{(-ln(x) + 1)}ln^{12}(x)}{x^{12}} - \frac{38678088{x}^{(-ln(x) + 1)}}{x^{12}}\\ \end{split}\end{equation} \]