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 10 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 10th\ derivative\ of\ function\ {ln(x)}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 10th\ derivative\ of\ function:} \\=&\frac{9{ln(x)}^{x}ln^{9}(ln(x))}{ln(x)} + \frac{9{ln(x)}^{x}ln^{8}(ln(x))}{ln^{2}(x)} + \frac{316{ln(x)}^{x}ln^{7}(ln(x))}{xln^{2}(x)} - \frac{9{ln(x)}^{x}ln^{8}(ln(x))}{xln^{2}(x)} + \frac{36{ln(x)}^{x}ln^{8}(ln(x))}{ln^{2}(x)} + \frac{36{ln(x)}^{x}ln^{7}(ln(x))}{ln^{3}(x)} - \frac{108{ln(x)}^{x}ln^{7}(ln(x))}{xln^{3}(x)} + \frac{308{ln(x)}^{x}ln^{6}(ln(x))}{xln^{3}(x)} - \frac{91{ln(x)}^{x}ln^{6}(ln(x))}{x^{2}ln^{2}(x)} + \frac{1386{ln(x)}^{x}ln^{5}(ln(x))}{x^{2}ln^{3}(x)} - \frac{476{ln(x)}^{x}ln^{6}(ln(x))}{x^{2}ln^{3}(x)} - \frac{28{ln(x)}^{x}ln^{7}(ln(x))}{x^{2}ln^{2}(x)} - \frac{36{ln(x)}^{x}ln^{8}(ln(x))}{xln^{2}(x)} + \frac{72{ln(x)}^{x}ln^{7}(ln(x))}{x^{2}ln^{3}(x)} + \frac{952{ln(x)}^{x}ln^{6}(ln(x))}{xln^{3}(x)} + \frac{84{ln(x)}^{x}ln^{7}(ln(x))}{ln^{3}(x)} + \frac{84{ln(x)}^{x}ln^{6}(ln(x))}{ln^{4}(x)} - \frac{504{ln(x)}^{x}ln^{6}(ln(x))}{xln^{4}(x)} + \frac{924{ln(x)}^{x}ln^{5}(ln(x))}{xln^{4}(x)} - \frac{252{ln(x)}^{x}ln^{7}(ln(x))}{xln^{3}(x)} + \frac{924{ln(x)}^{x}ln^{6}(ln(x))}{x^{2}ln^{4}(x)} - \frac{3192{ln(x)}^{x}ln^{5}(ln(x))}{x^{2}ln^{4}(x)} + \frac{1155{ln(x)}^{x}ln^{4}(ln(x))}{x^{2}ln^{4}(x)} - \frac{418{ln(x)}^{x}ln^{5}(ln(x))}{x^{3}ln^{2}(x)} - \frac{126{ln(x)}^{x}ln^{5}(ln(x))}{x^{2}ln^{3}(x)} - \frac{2875{ln(x)}^{x}ln^{4}(ln(x))}{x^{3}ln^{3}(x)} + \frac{882{ln(x)}^{x}ln^{5}(ln(x))}{x^{3}ln^{3}(x)} - \frac{1560{ln(x)}^{x}ln^{3}(ln(x))}{x^{3}ln^{4}(x)} + \frac{1995{ln(x)}^{x}ln^{4}(ln(x))}{x^{3}ln^{4}(x)} - \frac{784{ln(x)}^{x}ln^{6}(ln(x))}{x^{2}ln^{3}(x)} + \frac{868{ln(x)}^{x}ln^{5}(ln(x))}{x^{3}ln^{4}(x)} + \frac{126{ln(x)}^{x}ln^{6}(ln(x))}{x^{3}ln^{2}(x)} + \frac{28{ln(x)}^{x}ln^{7}(ln(x))}{x^{2}ln^{2}(x)} - \frac{112{ln(x)}^{x}ln^{6}(ln(x))}{x^{3}ln^{3}(x)} + \frac{168{ln(x)}^{x}ln^{7}(ln(x))}{x^{2}ln^{3}(x)} - \frac{504{ln(x)}^{x}ln^{6}(ln(x))}{x^{3}ln^{4}(x)} + \frac{4095{ln(x)}^{x}ln^{4}(ln(x))}{x^{2}ln^{4}(x)} + \frac{1596{ln(x)}^{x}ln^{5}(ln(x))}{xln^{4}(x)} + \frac{126{ln(x)}^{x}ln^{6}(ln(x))}{ln^{4}(x)} + \frac{126{ln(x)}^{x}ln^{5}(ln(x))}{ln^{5}(x)} - \frac{1260{ln(x)}^{x}ln^{5}(ln(x))}{xln^{5}(x)} + \frac{1540{ln(x)}^{x}ln^{4}(ln(x))}{xln^{5}(x)} - \frac{756{ln(x)}^{x}ln^{6}(ln(x))}{xln^{4}(x)} + \frac{4410{ln(x)}^{x}ln^{5}(ln(x))}{x^{2}ln^{5}(x)} - \frac{9800{ln(x)}^{x}ln^{4}(ln(x))}{x^{2}ln^{5}(x)} + \frac{3500{ln(x)}^{x}ln^{3}(ln(x))}{x^{2}ln^{5}(x)} - \frac{4368{ln(x)}^{x}ln^{5}(ln(x))}{x^{2}ln^{4}(x)} + \frac{1386{ln(x)}^{x}ln^{6}(ln(x))}{x^{2}ln^{4}(x)} - \frac{6300{ln(x)}^{x}ln^{5}(ln(x))}{x^{3}ln^{5}(x)} + \frac{13300{ln(x)}^{x}ln^{4}(ln(x))}{x^{3}ln^{5}(x)} - \frac{4200{ln(x)}^{x}ln^{3}(ln(x))}{x^{3}ln^{5}(x)} - \frac{2640{ln(x)}^{x}ln^{3}(ln(x))}{x^{3}ln^{4}(x)} - \frac{2090{ln(x)}^{x}ln^{2}(ln(x))}{x^{3}ln^{5}(x)} + \frac{2346{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{2}(x)} - \frac{275{ln(x)}^{x}ln^{4}(ln(x))}{x^{3}ln^{3}(x)} + \frac{4094{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{3}(x)} - \frac{1775{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{3}(x)} - \frac{2034{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{4}(x)} - \frac{960{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{4}(x)} + \frac{2898{ln(x)}^{x}ln^{5}(ln(x))}{x^{3}ln^{3}(x)} - \frac{6090{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{4}(x)} - \frac{2301{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{5}(x)} + \frac{12000{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{5}(x)} + \frac{4305{ln(x)}^{x}ln^{4}(ln(x))}{x^{3}ln^{4}(x)} - \frac{30450{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{5}(x)} - \frac{868{ln(x)}^{x}ln^{5}(ln(x))}{x^{3}ln^{4}(x)} + \frac{12600{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{5}(x)} - \frac{510{ln(x)}^{x}ln^{5}(ln(x))}{x^{4}ln^{2}(x)} + \frac{84{ln(x)}^{x}ln^{6}(ln(x))}{x^{3}ln^{2}(x)} - \frac{728{ln(x)}^{x}ln^{6}(ln(x))}{x^{3}ln^{3}(x)} + \frac{2520{ln(x)}^{x}ln^{5}(ln(x))}{x^{4}ln^{4}(x)} - \frac{756{ln(x)}^{x}ln^{6}(ln(x))}{x^{3}ln^{4}(x)} + \frac{3024{ln(x)}^{x}ln^{5}(ln(x))}{x^{4}ln^{5}(x)} + \frac{2090{ln(x)}^{x}ln^{2}(ln(x))}{x^{3}ln^{5}(x)} + \frac{4900{ln(x)}^{x}ln^{3}(ln(x))}{x^{2}ln^{5}(x)} + \frac{1610{ln(x)}^{x}ln^{4}(ln(x))}{xln^{5}(x)} + \frac{126{ln(x)}^{x}ln^{5}(ln(x))}{ln^{5}(x)} + \frac{126{ln(x)}^{x}ln^{4}(ln(x))}{ln^{6}(x)} - \frac{1890{ln(x)}^{x}ln^{4}(ln(x))}{xln^{6}(x)} + \frac{1540{ln(x)}^{x}ln^{3}(ln(x))}{xln^{6}(x)} - \frac{1260{ln(x)}^{x}ln^{5}(ln(x))}{xln^{5}(x)} + \frac{10710{ln(x)}^{x}ln^{4}(ln(x))}{x^{2}ln^{6}(x)} - \frac{15820{ln(x)}^{x}ln^{3}(ln(x))}{x^{2}ln^{6}(x)} + \frac{4095{ln(x)}^{x}ln^{2}(ln(x))}{x^{2}ln^{6}(x)} - \frac{9100{ln(x)}^{x}ln^{4}(ln(x))}{x^{2}ln^{5}(x)} + \frac{4410{ln(x)}^{x}ln^{5}(ln(x))}{x^{2}ln^{5}(x)} - \frac{28350{ln(x)}^{x}ln^{4}(ln(x))}{x^{3}ln^{6}(x)} + \frac{46900{ln(x)}^{x}ln^{3}(ln(x))}{x^{3}ln^{6}(x)} - \frac{17640{ln(x)}^{x}ln^{2}(ln(x))}{x^{3}ln^{6}(x)} + \frac{550{ln(x)}^{x}ln(ln(x))}{x^{3}ln^{6}(x)} - \frac{4200{ln(x)}^{x}ln^{3}(ln(x))}{x^{3}ln^{5}(x)} + \frac{8750{ln(x)}^{x}ln^{4}(ln(x))}{x^{3}ln^{5}(x)} - \frac{6300{ln(x)}^{x}ln^{5}(ln(x))}{x^{3}ln^{5}(x)} + \frac{34524{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{6}(x)} - \frac{7700{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{6}(x)} - \frac{34545{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{6}(x)} + \frac{14410{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{6}(x)} + \frac{4239{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{4}(x)} - \frac{9{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{5}(x)} - \frac{8376{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{2}(x)} - \frac{2594{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{3}(x)} + \frac{1786{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{3}(x)} + \frac{3952{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{3}(x)} + \frac{4620{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{4}(x)} - \frac{9{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{4}(x)} + \frac{19820{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{4}(x)} - \frac{7675{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{3}(x)} - \frac{16960{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{5}(x)} + \frac{48850{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{5}(x)} + \frac{960{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{4}(x)} + \frac{5300{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{6}(x)} + \frac{100170{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{6}(x)} - \frac{5460{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{4}(x)} + \frac{13200{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{5}(x)} - \frac{135800{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{6}(x)} - \frac{28350{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{5}(x)} + \frac{18900{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{5}(x)} + \frac{1976{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{2}(x)} + \frac{1100{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{3}(x)} - \frac{9660{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{4}(x)} - \frac{750{ln(x)}^{x}ln^{5}(ln(x))}{x^{4}ln^{2}(x)} - \frac{21840{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{5}(x)} + \frac{2520{ln(x)}^{x}ln^{5}(ln(x))}{x^{4}ln^{3}(x)} - \frac{15120{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{6}(x)} + \frac{5040{ln(x)}^{x}ln^{5}(ln(x))}{x^{4}ln^{4}(x)} + \frac{3024{ln(x)}^{x}ln^{5}(ln(x))}{x^{4}ln^{5}(x)} + \frac{1970{ln(x)}^{x}ln(ln(x))}{x^{3}ln^{6}(x)} + \frac{2835{ln(x)}^{x}ln^{2}(ln(x))}{x^{2}ln^{6}(x)} + \frac{14700{ln(x)}^{x}ln^{3}(ln(x))}{x^{2}ln^{7}(x)} - \frac{14028{ln(x)}^{x}ln^{2}(ln(x))}{x^{2}ln^{7}(x)} + \frac{980{ln(x)}^{x}ln^{3}(ln(x))}{xln^{6}(x)} - \frac{1260{ln(x)}^{x}ln^{4}(ln(x))}{xln^{6}(x)} - \frac{1764{ln(x)}^{x}ln^{3}(ln(x))}{xln^{7}(x)} + \frac{924{ln(x)}^{x}ln^{2}(ln(x))}{xln^{7}(x)} + \frac{2226{ln(x)}^{x}ln(ln(x))}{x^{2}ln^{7}(x)} + \frac{84{ln(x)}^{x}ln^{4}(ln(x))}{ln^{6}(x)} + \frac{84{ln(x)}^{x}ln^{3}(ln(x))}{ln^{7}(x)} - \frac{61740{ln(x)}^{x}ln^{3}(ln(x))}{x^{3}ln^{7}(x)} + \frac{71260{ln(x)}^{x}ln^{2}(ln(x))}{x^{3}ln^{7}(x)} - \frac{9380{ln(x)}^{x}ln^{3}(ln(x))}{x^{2}ln^{6}(x)} + \frac{7140{ln(x)}^{x}ln^{4}(ln(x))}{x^{2}ln^{6}(x)} - \frac{18354{ln(x)}^{x}ln(ln(x))}{x^{3}ln^{7}(x)} - \frac{10710{ln(x)}^{x}ln^{2}(ln(x))}{x^{3}ln^{6}(x)} + \frac{136416{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{7}(x)} - \frac{104580{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{7}(x)} + \frac{24500{ln(x)}^{x}ln^{3}(ln(x))}{x^{3}ln^{6}(x)} + \frac{6720{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{7}(x)} - \frac{18900{ln(x)}^{x}ln^{4}(ln(x))}{x^{3}ln^{6}(x)} + \frac{4490{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{6}(x)} - \frac{19005{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{6}(x)} - \frac{148176{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{7}(x)} - \frac{204904{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{7}(x)} + \frac{179760{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{7}(x)} + \frac{7700{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{6}(x)} + \frac{23016{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{6}(x)} - \frac{4620{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{4}(x)} + \frac{22740{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{2}(x)} - \frac{5616{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{3}(x)} - \frac{8838{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{3}(x)} + \frac{1152{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{4}(x)} - \frac{49086{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{4}(x)} - \frac{61315{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{5}(x)} - \frac{6226{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{3}(x)} - \frac{10700{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{5}(x)} - \frac{210460{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{6}(x)} + \frac{330960{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{6}(x)} + \frac{16208{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{3}(x)} - \frac{13221{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{4}(x)} - \frac{10340{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{5}(x)} + \frac{84924{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{7}(x)} + \frac{26380{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{4}(x)} + \frac{39350{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{5}(x)} + \frac{701568{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{7}(x)} - \frac{29400{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{5}(x)} - \frac{5300{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{6}(x)} - \frac{7016{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{2}(x)} - \frac{6168{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{3}(x)} + \frac{31560{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{4}(x)} + \frac{41580{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{6}(x)} + \frac{100800{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{5}(x)} + \frac{124320{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{6}(x)} - \frac{94360{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{6}(x)} + \frac{3484{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{2}(x)} - \frac{7400{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{3}(x)} + \frac{60480{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{7}(x)} - \frac{21840{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{4}(x)} + \frac{243684{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{8}(x)} - \frac{12600{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{5}(x)} - \frac{152880{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{8}(x)} - \frac{5586{ln(x)}^{x}ln(ln(x))}{x^{3}ln^{7}(x)} - \frac{23520{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{5}(x)} - \frac{70560{ln(x)}^{x}ln^{2}(ln(x))}{x^{3}ln^{8}(x)} + \frac{50008{ln(x)}^{x}ln(ln(x))}{x^{3}ln^{8}(x)} - \frac{10080{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln^{6}(x)} + \frac{23240{ln(x)}^{x}ln^{2}(ln(x))}{x^{3}ln^{7}(x)} + \frac{714{ln(x)}^{x}ln(ln(x))}{x^{2}ln^{7}(x)} - \frac{26460{ln(x)}^{x}ln^{3}(ln(x))}{x^{3}ln^{7}(x)} + \frac{11592{ln(x)}^{x}ln^{2}(ln(x))}{x^{2}ln^{8}(x)} - \frac{6496{ln(x)}^{x}ln(ln(x))}{x^{2}ln^{8}(x)} - \frac{472752{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{8}(x)} + \frac{1092{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{8}(x)} - \frac{4872{ln(x)}^{x}ln^{2}(ln(x))}{x^{2}ln^{7}(x)} + \frac{3780{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{7}(x)} + \frac{6300{ln(x)}^{x}ln^{3}(ln(x))}{x^{2}ln^{7}(x)} + \frac{470448{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{8}(x)} + \frac{1026256{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{8}(x)} + \frac{336{ln(x)}^{x}ln^{2}(ln(x))}{xln^{7}(x)} - \frac{1008{ln(x)}^{x}ln^{2}(ln(x))}{xln^{8}(x)} + \frac{308{ln(x)}^{x}ln(ln(x))}{xln^{8}(x)} - \frac{756{ln(x)}^{x}ln^{3}(ln(x))}{xln^{7}(x)} - \frac{45360{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{2}(x)} + \frac{16956{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{3}(x)} - \frac{27720{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{7}(x)} + \frac{58464{ln(x)}^{x}ln^{3}(ln(x))}{x^{4}ln^{7}(x)} + \frac{91234{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{4}(x)} + \frac{40740{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{7}(x)} + \frac{66750{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{5}(x)} - \frac{543420{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{6}(x)} - \frac{1675296{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{7}(x)} - \frac{63504{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{7}(x)} - \frac{87416{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{7}(x)} + \frac{15056{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{3}(x)} - \frac{2050128{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{8}(x)} + \frac{21492{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{2}(x)} + \frac{36{ln(x)}^{x}ln^{3}(ln(x))}{ln^{7}(x)} + \frac{36{ln(x)}^{x}ln^{2}(ln(x))}{ln^{8}(x)} + \frac{21084{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{3}(x)} - \frac{87804{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{4}(x)} - \frac{340560{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{5}(x)} - \frac{25182{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{3}(x)} + \frac{25308{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{4}(x)} - \frac{65259{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{4}(x)} - \frac{19535{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{5}(x)} - \frac{559440{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{6}(x)} + \frac{10700{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{5}(x)} - \frac{73040{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{6}(x)} - \frac{483840{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{7}(x)} - \frac{181440{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{8}(x)} - \frac{11464{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{2}(x)} + \frac{186900{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{6}(x)} + \frac{12516{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{7}(x)} + \frac{17928{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{3}(x)} + \frac{1063116{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{9}(x)} + \frac{250992{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{7}(x)} - \frac{605556{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{9}(x)} + \frac{69240{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{4}(x)} - \frac{986256{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{9}(x)} - \frac{51336{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{2}(x)} - \frac{42088{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{3}(x)} + \frac{199164{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{4}(x)} + \frac{100800{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{5}(x)} + \frac{808584{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{5}(x)} + \frac{1543920{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{6}(x)} + \frac{1774080{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{7}(x)} + \frac{77280{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{6}(x)} + \frac{202041{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{9}(x)} + \frac{1189440{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{8}(x)} + \frac{25920{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln^{7}(x)} - \frac{1092{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{8}(x)} + \frac{362880{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{9}(x)} - \frac{23520{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{8}(x)} + \frac{25488{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{2}(x)} + \frac{22764{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{3}(x)} - \frac{118188{ln(x)}^{x}ln^{2}(ln(x))}{x^{5}ln^{8}(x)} - \frac{50400{ln(x)}^{x}ln(ln(x))}{x^{8}ln(x)} + \frac{155624{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{8}(x)} + \frac{60921{ln(x)}^{x}ln^{2}(ln(x))}{x^{4}ln^{8}(x)} - \frac{33684{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{3}(x)} + \frac{88946{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{4}(x)} - \frac{28944{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{2}(x)} + \frac{117612{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{8}(x)} + \frac{31680{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{2}(x)} - \frac{152226{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{4}(x)} + \frac{48750{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{5}(x)} - \frac{40824{ln(x)}^{x}ln(ln(x))}{x^{3}ln^{9}(x)} + \frac{32400{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln(x)} - \frac{14280{ln(x)}^{x}ln^{2}(ln(x))}{x^{6}ln^{2}(x)} - \frac{264240{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{5}(x)} - \frac{147060{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{6}(x)} + \frac{40808{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{3}(x)} - \frac{272160{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{6}(x)} - \frac{335664{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{7}(x)} + \frac{7952{ln(x)}^{x}ln(ln(x))}{x^{3}ln^{8}(x)} - \frac{14400{ln(x)}^{x}ln^{3}(ln(x))}{x^{6}ln(x)} + \frac{182616{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{4}(x)} + \frac{5016{ln(x)}^{x}ln^{3}(ln(x))}{x^{5}ln^{2}(x)} + \frac{5040{ln(x)}^{x}ln^{4}(ln(x))}{x^{5}ln(x)} - \frac{17640{ln(x)}^{x}ln^{2}(ln(x))}{x^{3}ln^{8}(x)} - \frac{164160{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{7}(x)} - \frac{302112{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{8}(x)} + \frac{345576{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{5}(x)} - \frac{1506{ln(x)}^{x}ln^{4}(ln(x))}{x^{4}ln^{2}(x)} - \frac{1512{ln(x)}^{x}ln^{5}(ln(x))}{x^{4}ln(x)} - \frac{45360{ln(x)}^{x}ln^{2}(ln(x))}{x^{7}ln^{8}(x)} + \frac{421680{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{6}(x)} + \frac{418{ln(x)}^{x}ln^{5}(ln(x))}{x^{3}ln^{2}(x)} + \frac{420{ln(x)}^{x}ln^{6}(ln(x))}{x^{3}ln(x)} + \frac{4914{ln(x)}^{x}ln(ln(x))}{x^{2}ln^{9}(x)} + \frac{342720{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{7}(x)} - \frac{119{ln(x)}^{x}ln^{6}(ln(x))}{x^{2}ln^{2}(x)} - \frac{120{ln(x)}^{x}ln^{7}(ln(x))}{x^{2}ln(x)} - \frac{1064{ln(x)}^{x}ln(ln(x))}{x^{2}ln^{8}(x)} + \frac{171360{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{8}(x)} + \frac{52{ln(x)}^{x}ln(ln(x))}{xln^{8}(x)} - \frac{324{ln(x)}^{x}ln(ln(x))}{xln^{9}(x)} + \frac{44{ln(x)}^{x}ln^{7}(ln(x))}{xln^{2}(x)} + \frac{45{ln(x)}^{x}ln^{8}(ln(x))}{xln(x)} + \frac{2898{ln(x)}^{x}ln^{2}(ln(x))}{x^{2}ln^{8}(x)} - \frac{252{ln(x)}^{x}ln^{2}(ln(x))}{xln^{8}(x)} - \frac{36{ln(x)}^{x}ln(ln(x))}{xln^{9}(x)} + \frac{546{ln(x)}^{x}ln(ln(x))}{x^{2}ln^{9}(x)} - \frac{4536{ln(x)}^{x}ln(ln(x))}{x^{3}ln^{9}(x)} + \frac{22449{ln(x)}^{x}ln(ln(x))}{x^{4}ln^{9}(x)} - \frac{67284{ln(x)}^{x}ln(ln(x))}{x^{5}ln^{9}(x)} + \frac{118124{ln(x)}^{x}ln(ln(x))}{x^{6}ln^{9}(x)} - \frac{109584{ln(x)}^{x}ln(ln(x))}{x^{7}ln^{9}(x)} + \frac{40320{ln(x)}^{x}ln(ln(x))}{x^{8}ln^{9}(x)} + \frac{510{ln(x)}^{x}}{x^{2}ln^{8}(x)} + \frac{420042{ln(x)}^{x}}{x^{8}ln^{6}(x)} + \frac{19320{ln(x)}^{x}}{x^{4}ln^{8}(x)} + \frac{1852200{ln(x)}^{x}}{x^{8}ln^{7}(x)} - \frac{21540{ln(x)}^{x}}{x^{7}ln^{4}(x)} - \frac{110250{ln(x)}^{x}}{x^{6}ln^{7}(x)} - \frac{987{ln(x)}^{x}}{x^{4}ln^{6}(x)} - \frac{68040{ln(x)}^{x}}{x^{4}ln^{9}(x)} + \frac{33075{ln(x)}^{x}}{x^{7}ln^{5}(x)} + \frac{3136320{ln(x)}^{x}}{x^{8}ln^{8}(x)} + \frac{58800{ln(x)}^{x}}{x^{5}ln^{8}(x)} + \frac{222075{ln(x)}^{x}}{x^{7}ln^{6}(x)} + \frac{2739600{ln(x)}^{x}}{x^{8}ln^{9}(x)} - \frac{820{ln(x)}^{x}}{x^{6}ln^{4}(x)} + \frac{1050{ln(x)}^{x}}{x^{3}ln^{7}(x)} + \frac{146160{ln(x)}^{x}}{x^{7}ln^{7}(x)} - \frac{1260{ln(x)}^{x}}{x^{2}ln^{9}(x)} + \frac{23205{ln(x)}^{x}}{x^{6}ln^{6}(x)} - \frac{26250{ln(x)}^{x}}{x^{5}ln^{7}(x)} + \frac{11016{ln(x)}^{x}}{x^{8}ln^{2}(x)} + \frac{336420{ln(x)}^{x}}{x^{6}ln^{9}(x)} - \frac{203070{ln(x)}^{x}}{x^{6}ln^{8}(x)} - \frac{787920{ln(x)}^{x}}{x^{7}ln^{8}(x)} - \frac{1771860{ln(x)}^{x}}{x^{7}ln^{9}(x)} + \frac{1890{ln(x)}^{x}}{x^{4}ln^{7}(x)} + \frac{112245{ln(x)}^{x}}{x^{5}ln^{9}(x)} + \frac{9{ln(x)}^{x}ln^{2}(ln(x))}{ln^{8}(x)} + \frac{9{ln(x)}^{x}ln(ln(x))}{ln^{9}(x)} + \frac{45{ln(x)}^{x}}{xln^{9}(x)} - \frac{6720{ln(x)}^{x}}{x^{3}ln^{8}(x)} + \frac{{ln(x)}^{x}ln^{9}(ln(x))}{ln(x)} + \frac{{ln(x)}^{x}ln(ln(x))}{ln^{9}(x)} + {ln(x)}^{x}ln^{10}(ln(x)) + \frac{{ln(x)}^{x}}{ln^{10}(x)} - \frac{45{ln(x)}^{x}}{xln^{10}(x)} - \frac{4095{ln(x)}^{x}}{x^{5}ln^{6}(x)} + \frac{870{ln(x)}^{x}}{x^{2}ln^{10}(x)} + \frac{13650{ln(x)}^{x}}{x^{3}ln^{9}(x)} - \frac{9450{ln(x)}^{x}}{x^{3}ln^{10}(x)} - \frac{23700{ln(x)}^{x}}{x^{8}ln^{3}(x)} + \frac{63273{ln(x)}^{x}}{x^{4}ln^{10}(x)} + \frac{13650{ln(x)}^{x}}{x^{6}ln^{5}(x)} - \frac{269325{ln(x)}^{x}}{x^{5}ln^{10}(x)} - \frac{140690{ln(x)}^{x}}{x^{8}ln^{4}(x)} + \frac{723680{ln(x)}^{x}}{x^{6}ln^{10}(x)} - \frac{5340{ln(x)}^{x}}{x^{7}ln^{3}(x)} - \frac{1172700{ln(x)}^{x}}{x^{7}ln^{10}(x)} + \frac{1365{ln(x)}^{x}}{x^{5}ln^{5}(x)} + \frac{1026576{ln(x)}^{x}}{x^{8}ln^{10}(x)} + \frac{40320{ln(x)}^{x}}{x^{9}ln(x)} + \frac{69264{ln(x)}^{x}}{x^{9}ln^{2}(x)} + \frac{17080{ln(x)}^{x}}{x^{9}ln^{3}(x)} - \frac{305040{ln(x)}^{x}}{x^{9}ln^{4}(x)} - \frac{1076040{ln(x)}^{x}}{x^{9}ln^{5}(x)} - \frac{2149560{ln(x)}^{x}}{x^{9}ln^{6}(x)} - \frac{2872800{ln(x)}^{x}}{x^{9}ln^{7}(x)} - \frac{2570400{ln(x)}^{x}}{x^{9}ln^{8}(x)} - \frac{1411200{ln(x)}^{x}}{x^{9}ln^{9}(x)} - \frac{162750{ln(x)}^{x}}{x^{8}ln^{5}(x)} - \frac{362880{ln(x)}^{x}}{x^{9}ln^{10}(x)}\\ \end{split}\end{equation} \]