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 15 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ {x}^{ln(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&\frac{-26337645981360{x}^{ln(x)}ln(x)ln(x)}{x^{15}} + \frac{24416012857728{x}^{ln(x)}ln^{2}(x)ln(x)}{x^{15}} + \frac{24416012857728{x}^{ln(x)}ln^{2}(x)ln(x)}{x^{15}} - \frac{26337645981360{x}^{ln(x)}ln(x)ln(x)}{x^{15}} - \frac{13639109129100{x}^{ln(x)}ln^{3}(x)ln(x)}{x^{15}} - \frac{15977844628200{x}^{ln(x)}ln^{2}(x)ln^{2}(x)}{x^{15}} + \frac{18057725045424{x}^{ln(x)}ln(x)ln^{2}(x)}{x^{15}} - \frac{15977844628200{x}^{ln(x)}ln^{2}(x)ln^{2}(x)}{x^{15}} - \frac{13639109129100{x}^{ln(x)}ln^{3}(x)ln(x)}{x^{15}} + \frac{18057725045424{x}^{ln(x)}ln(x)ln^{2}(x)}{x^{15}} + \frac{5175704468480{x}^{ln(x)}ln^{4}(x)ln(x)}{x^{15}} + \frac{6451596525920{x}^{ln(x)}ln^{2}(x)ln^{3}(x)}{x^{15}} + \frac{8401502731440{x}^{ln(x)}ln^{3}(x)ln^{2}(x)}{x^{15}} + \frac{8401502731440{x}^{ln(x)}ln^{3}(x)ln^{2}(x)}{x^{15}} - \frac{7664683708500{x}^{ln(x)}ln(x)ln^{3}(x)}{x^{15}} + \frac{6451596525920{x}^{ln(x)}ln^{2}(x)ln^{3}(x)}{x^{15}} + \frac{5175704468480{x}^{ln(x)}ln^{4}(x)ln(x)}{x^{15}} - \frac{7664683708500{x}^{ln(x)}ln(x)ln^{3}(x)}{x^{15}} - \frac{1419567048900{x}^{ln(x)}ln^{5}(x)ln(x)}{x^{15}} - \frac{1794865997925{x}^{ln(x)}ln^{2}(x)ln^{4}(x)}{x^{15}} - \frac{2964233747475{x}^{ln(x)}ln^{4}(x)ln^{2}(x)}{x^{15}} - \frac{3172733163600{x}^{ln(x)}ln^{3}(x)ln^{3}(x)}{x^{15}} + \frac{2250845160200{x}^{ln(x)}ln(x)ln^{4}(x)}{x^{15}} - \frac{3172733163600{x}^{ln(x)}ln^{3}(x)ln^{3}(x)}{x^{15}} - \frac{2964233747475{x}^{ln(x)}ln^{4}(x)ln^{2}(x)}{x^{15}} - \frac{1794865997925{x}^{ln(x)}ln^{2}(x)ln^{4}(x)}{x^{15}} - \frac{1419567048900{x}^{ln(x)}ln^{5}(x)ln(x)}{x^{15}} + \frac{2250845160200{x}^{ln(x)}ln(x)ln^{4}(x)}{x^{15}} + \frac{291353230168{x}^{ln(x)}ln^{6}(x)ln(x)}{x^{15}} + \frac{363702867528{x}^{ln(x)}ln^{2}(x)ln^{5}(x)}{x^{15}} + \frac{746470484760{x}^{ln(x)}ln^{5}(x)ln^{2}(x)}{x^{15}} + \frac{818820122120{x}^{ln(x)}ln^{3}(x)ln^{4}(x)}{x^{15}} - \frac{484072849260{x}^{ln(x)}ln(x)ln^{5}(x)}{x^{15}} + \frac{1031468798360{x}^{ln(x)}ln^{4}(x)ln^{3}(x)}{x^{15}} + \frac{1031468798360{x}^{ln(x)}ln^{4}(x)ln^{3}(x)}{x^{15}} + \frac{818820122120{x}^{ln(x)}ln^{3}(x)ln^{4}(x)}{x^{15}} + \frac{746470484760{x}^{ln(x)}ln^{5}(x)ln^{2}(x)}{x^{15}} + \frac{363702867528{x}^{ln(x)}ln^{2}(x)ln^{5}(x)}{x^{15}} + \frac{291353230168{x}^{ln(x)}ln^{6}(x)ln(x)}{x^{15}} - \frac{484072849260{x}^{ln(x)}ln(x)ln^{5}(x)}{x^{15}} - \frac{45586365825{x}^{ln(x)}ln^{7}(x)ln(x)}{x^{15}} - \frac{55302572325{x}^{ln(x)}ln^{2}(x)ln^{6}(x)}{x^{15}} - \frac{138702338775{x}^{ln(x)}ln^{6}(x)ln^{2}(x)}{x^{15}} - \frac{152305027875{x}^{ln(x)}ln^{3}(x)ln^{5}(x)}{x^{15}} + \frac{78704553928{x}^{ln(x)}ln(x)ln^{6}(x)}{x^{15}} - \frac{235704794325{x}^{ln(x)}ln^{5}(x)ln^{3}(x)}{x^{15}} - \frac{242506138875{x}^{ln(x)}ln^{4}(x)ln^{4}(x)}{x^{15}} - \frac{242506138875{x}^{ln(x)}ln^{4}(x)ln^{4}(x)}{x^{15}} - \frac{235704794325{x}^{ln(x)}ln^{5}(x)ln^{3}(x)}{x^{15}} - \frac{152305027875{x}^{ln(x)}ln^{3}(x)ln^{5}(x)}{x^{15}} - \frac{138702338775{x}^{ln(x)}ln^{6}(x)ln^{2}(x)}{x^{15}} - \frac{55302572325{x}^{ln(x)}ln^{2}(x)ln^{6}(x)}{x^{15}} - \frac{45586365825{x}^{ln(x)}ln^{7}(x)ln(x)}{x^{15}} + \frac{78704553928{x}^{ln(x)}ln(x)ln^{6}(x)}{x^{15}} + \frac{5475848950{x}^{ln(x)}ln^{8}(x)ln(x)}{x^{15}} + \frac{6399902080{x}^{ln(x)}ln^{2}(x)ln^{7}(x)}{x^{15}} + \frac{19319480180{x}^{ln(x)}ln^{7}(x)ln^{2}(x)}{x^{15}} + \frac{20962241300{x}^{ln(x)}ln^{3}(x)ln^{6}(x)}{x^{15}} - \frac{9843608775{x}^{ln(x)}ln(x)ln^{7}(x)}{x^{15}} + \frac{39049650640{x}^{ln(x)}ln^{6}(x)ln^{3}(x)}{x^{15}} + \frac{40487066620{x}^{ln(x)}ln^{4}(x)ln^{5}(x)}{x^{15}} + \frac{49530771290{x}^{ln(x)}ln^{5}(x)ln^{4}(x)}{x^{15}} + \frac{49530771290{x}^{ln(x)}ln^{5}(x)ln^{4}(x)}{x^{15}} + \frac{40487066620{x}^{ln(x)}ln^{4}(x)ln^{5}(x)}{x^{15}} + \frac{39049650640{x}^{ln(x)}ln^{6}(x)ln^{3}(x)}{x^{15}} + \frac{20962241300{x}^{ln(x)}ln^{3}(x)ln^{6}(x)}{x^{15}} + \frac{19319480180{x}^{ln(x)}ln^{7}(x)ln^{2}(x)}{x^{15}} + \frac{6399902080{x}^{ln(x)}ln^{2}(x)ln^{7}(x)}{x^{15}} + \frac{5475848950{x}^{ln(x)}ln^{8}(x)ln(x)}{x^{15}} - \frac{9843608775{x}^{ln(x)}ln(x)ln^{7}(x)}{x^{15}} - \frac{503377875{x}^{ln(x)}ln^{9}(x)ln(x)}{x^{15}} - \frac{564864300{x}^{ln(x)}ln^{2}(x)ln^{8}(x)}{x^{15}} - \frac{2022295275{x}^{ln(x)}ln^{8}(x)ln^{2}(x)}{x^{15}} - \frac{2154051900{x}^{ln(x)}ln^{3}(x)ln^{7}(x)}{x^{15}} + \frac{953996615{x}^{ln(x)}ln(x)ln^{8}(x)}{x^{15}} - \frac{4745040300{x}^{ln(x)}ln^{7}(x)ln^{3}(x)}{x^{15}} - \frac{4903148250{x}^{ln(x)}ln^{4}(x)ln^{6}(x)}{x^{15}} - \frac{7170263100{x}^{ln(x)}ln^{6}(x)ln^{4}(x)}{x^{15}} - \frac{7244046810{x}^{ln(x)}ln^{5}(x)ln^{5}(x)}{x^{15}} - \frac{7244046810{x}^{ln(x)}ln^{5}(x)ln^{5}(x)}{x^{15}} - \frac{7170263100{x}^{ln(x)}ln^{6}(x)ln^{4}(x)}{x^{15}} - \frac{4903148250{x}^{ln(x)}ln^{4}(x)ln^{6}(x)}{x^{15}} - \frac{4745040300{x}^{ln(x)}ln^{7}(x)ln^{3}(x)}{x^{15}} - \frac{2154051900{x}^{ln(x)}ln^{3}(x)ln^{7}(x)}{x^{15}} - \frac{2022295275{x}^{ln(x)}ln^{8}(x)ln^{2}(x)}{x^{15}} + \frac{953996615{x}^{ln(x)}ln(x)ln^{8}(x)}{x^{15}} - \frac{564864300{x}^{ln(x)}ln^{2}(x)ln^{8}(x)}{x^{15}} - \frac{503377875{x}^{ln(x)}ln^{9}(x)ln(x)}{x^{15}} + \frac{34908874{x}^{ln(x)}ln^{10}(x)ln(x)}{x^{15}} + \frac{37647610{x}^{ln(x)}ln^{2}(x)ln^{9}(x)}{x^{15}} + \frac{157432275{x}^{ln(x)}ln^{9}(x)ln^{2}(x)}{x^{15}} + \frac{164279115{x}^{ln(x)}ln^{3}(x)ln^{8}(x)}{x^{15}} - \frac{71546475{x}^{ln(x)}ln(x)ln^{9}(x)}{x^{15}} + \frac{420960540{x}^{ln(x)}ln^{8}(x)ln^{3}(x)}{x^{15}} + \frac{431230800{x}^{ln(x)}ln^{4}(x)ln^{7}(x)}{x^{15}} + \frac{739248510{x}^{ln(x)}ln^{7}(x)ln^{4}(x)}{x^{15}} + \frac{747464718{x}^{ln(x)}ln^{5}(x)ln^{6}(x)}{x^{15}} + \frac{891206316{x}^{ln(x)}ln^{6}(x)ln^{5}(x)}{x^{15}} + \frac{891206316{x}^{ln(x)}ln^{6}(x)ln^{5}(x)}{x^{15}} + \frac{747464718{x}^{ln(x)}ln^{5}(x)ln^{6}(x)}{x^{15}} + \frac{739248510{x}^{ln(x)}ln^{7}(x)ln^{4}(x)}{x^{15}} - \frac{71546475{x}^{ln(x)}ln(x)ln^{9}(x)}{x^{15}} + \frac{431230800{x}^{ln(x)}ln^{4}(x)ln^{7}(x)}{x^{15}} + \frac{420960540{x}^{ln(x)}ln^{8}(x)ln^{3}(x)}{x^{15}} + \frac{164279115{x}^{ln(x)}ln^{3}(x)ln^{8}(x)}{x^{15}} + \frac{157432275{x}^{ln(x)}ln^{9}(x)ln^{2}(x)}{x^{15}} + \frac{37647610{x}^{ln(x)}ln^{2}(x)ln^{9}(x)}{x^{15}} + \frac{34908874{x}^{ln(x)}ln^{10}(x)ln(x)}{x^{15}} - \frac{1773135{x}^{ln(x)}ln^{11}(x)ln(x)}{x^{15}} - \frac{1846845{x}^{ln(x)}ln^{2}(x)ln^{10}(x)}{x^{15}} - \frac{8873865{x}^{ln(x)}ln^{10}(x)ln^{2}(x)}{x^{15}} - \frac{9084075{x}^{ln(x)}ln^{3}(x)ln^{9}(x)}{x^{15}} + \frac{4107103{x}^{ln(x)}ln(x)ln^{10}(x)}{x^{15}} - \frac{26651625{x}^{ln(x)}ln^{9}(x)ln^{3}(x)}{x^{15}} - \frac{27027000{x}^{ln(x)}ln^{4}(x)ln^{8}(x)}{x^{15}} - \frac{53378325{x}^{ln(x)}ln^{8}(x)ln^{4}(x)}{x^{15}} - \frac{53783730{x}^{ln(x)}ln^{5}(x)ln^{7}(x)}{x^{15}} - \frac{74864790{x}^{ln(x)}ln^{7}(x)ln^{5}(x)}{x^{15}} - \frac{75044970{x}^{ln(x)}ln^{6}(x)ln^{6}(x)}{x^{15}} + \frac{4107103{x}^{ln(x)}ln(x)ln^{10}(x)}{x^{15}} - \frac{75044970{x}^{ln(x)}ln^{6}(x)ln^{6}(x)}{x^{15}} - \frac{74864790{x}^{ln(x)}ln^{7}(x)ln^{5}(x)}{x^{15}} - \frac{53783730{x}^{ln(x)}ln^{5}(x)ln^{7}(x)}{x^{15}} - \frac{53378325{x}^{ln(x)}ln^{8}(x)ln^{4}(x)}{x^{15}} - \frac{27027000{x}^{ln(x)}ln^{4}(x)ln^{8}(x)}{x^{15}} - \frac{26651625{x}^{ln(x)}ln^{9}(x)ln^{3}(x)}{x^{15}} - \frac{9084075{x}^{ln(x)}ln^{3}(x)ln^{9}(x)}{x^{15}} - \frac{8873865{x}^{ln(x)}ln^{10}(x)ln^{2}(x)}{x^{15}} - \frac{1846845{x}^{ln(x)}ln^{2}(x)ln^{10}(x)}{x^{15}} - \frac{1773135{x}^{ln(x)}ln^{11}(x)ln(x)}{x^{15}} + \frac{62426{x}^{ln(x)}ln^{12}(x)ln(x)}{x^{15}} + \frac{63336{x}^{ln(x)}ln^{2}(x)ln^{11}(x)}{x^{15}} + \frac{343434{x}^{ln(x)}ln^{11}(x)ln^{2}(x)}{x^{15}} + \frac{346346{x}^{ln(x)}ln^{3}(x)ln^{10}(x)}{x^{15}} - \frac{176085{x}^{ln(x)}ln(x)ln^{11}(x)}{x^{15}} + \frac{1145144{x}^{ln(x)}ln^{10}(x)ln^{3}(x)}{x^{15}} + \frac{1151150{x}^{ln(x)}ln^{4}(x)ln^{9}(x)}{x^{15}} + \frac{2577575{x}^{ln(x)}ln^{9}(x)ln^{4}(x)}{x^{15}} + \frac{2585583{x}^{ln(x)}ln^{5}(x)ln^{8}(x)}{x^{15}} - \frac{176085{x}^{ln(x)}ln(x)ln^{11}(x)}{x^{15}} + \frac{4126122{x}^{ln(x)}ln^{8}(x)ln^{5}(x)}{x^{15}} + \frac{4132128{x}^{ln(x)}ln^{6}(x)ln^{7}(x)}{x^{15}} + \frac{4816812{x}^{ln(x)}ln^{7}(x)ln^{6}(x)}{x^{15}} + \frac{4816812{x}^{ln(x)}ln^{7}(x)ln^{6}(x)}{x^{15}} + \frac{4132128{x}^{ln(x)}ln^{6}(x)ln^{7}(x)}{x^{15}} + \frac{4126122{x}^{ln(x)}ln^{8}(x)ln^{5}(x)}{x^{15}} + \frac{2585583{x}^{ln(x)}ln^{5}(x)ln^{8}(x)}{x^{15}} + \frac{2577575{x}^{ln(x)}ln^{9}(x)ln^{4}(x)}{x^{15}} + \frac{1151150{x}^{ln(x)}ln^{4}(x)ln^{9}(x)}{x^{15}} + \frac{1145144{x}^{ln(x)}ln^{10}(x)ln^{3}(x)}{x^{15}} + \frac{346346{x}^{ln(x)}ln^{3}(x)ln^{10}(x)}{x^{15}} + \frac{343434{x}^{ln(x)}ln^{11}(x)ln^{2}(x)}{x^{15}} + \frac{63336{x}^{ln(x)}ln^{2}(x)ln^{11}(x)}{x^{15}} + \frac{62426{x}^{ln(x)}ln^{12}(x)ln(x)}{x^{15}} - \frac{1365{x}^{ln(x)}ln^{13}(x)ln(x)}{x^{15}} - \frac{1365{x}^{ln(x)}ln^{2}(x)ln^{12}(x)}{x^{15}} - \frac{8190{x}^{ln(x)}ln^{12}(x)ln^{2}(x)}{x^{15}} - \frac{8190{x}^{ln(x)}ln^{3}(x)ln^{11}(x)}{x^{15}} + \frac{5369{x}^{ln(x)}ln(x)ln^{12}(x)}{x^{15}} - \frac{30030{x}^{ln(x)}ln^{11}(x)ln^{3}(x)}{x^{15}} - \frac{30030{x}^{ln(x)}ln^{4}(x)ln^{10}(x)}{x^{15}} + \frac{5369{x}^{ln(x)}ln(x)ln^{12}(x)}{x^{15}} - \frac{75075{x}^{ln(x)}ln^{10}(x)ln^{4}(x)}{x^{15}} - \frac{75075{x}^{ln(x)}ln^{5}(x)ln^{9}(x)}{x^{15}} - \frac{135135{x}^{ln(x)}ln^{9}(x)ln^{5}(x)}{x^{15}} - \frac{135135{x}^{ln(x)}ln^{6}(x)ln^{8}(x)}{x^{15}} - \frac{180180{x}^{ln(x)}ln^{8}(x)ln^{6}(x)}{x^{15}} - \frac{180180{x}^{ln(x)}ln^{7}(x)ln^{7}(x)}{x^{15}} - \frac{180180{x}^{ln(x)}ln^{7}(x)ln^{7}(x)}{x^{15}} - \frac{180180{x}^{ln(x)}ln^{8}(x)ln^{6}(x)}{x^{15}} - \frac{135135{x}^{ln(x)}ln^{6}(x)ln^{8}(x)}{x^{15}} - \frac{135135{x}^{ln(x)}ln^{9}(x)ln^{5}(x)}{x^{15}} - \frac{75075{x}^{ln(x)}ln^{5}(x)ln^{9}(x)}{x^{15}} - \frac{75075{x}^{ln(x)}ln^{10}(x)ln^{4}(x)}{x^{15}} - \frac{30030{x}^{ln(x)}ln^{4}(x)ln^{10}(x)}{x^{15}} - \frac{30030{x}^{ln(x)}ln^{11}(x)ln^{3}(x)}{x^{15}} - \frac{8190{x}^{ln(x)}ln^{3}(x)ln^{11}(x)}{x^{15}} - \frac{8190{x}^{ln(x)}ln^{12}(x)ln^{2}(x)}{x^{15}} - \frac{1365{x}^{ln(x)}ln^{2}(x)ln^{12}(x)}{x^{15}} - \frac{1365{x}^{ln(x)}ln^{13}(x)ln(x)}{x^{15}} + \frac{14{x}^{ln(x)}ln^{14}(x)ln(x)}{x^{15}} + \frac{14{x}^{ln(x)}ln^{2}(x)ln^{13}(x)}{x^{15}} - \frac{105{x}^{ln(x)}ln(x)ln^{13}(x)}{x^{15}} + \frac{91{x}^{ln(x)}ln^{13}(x)ln^{2}(x)}{x^{15}} + \frac{91{x}^{ln(x)}ln^{3}(x)ln^{12}(x)}{x^{15}} - \frac{105{x}^{ln(x)}ln(x)ln^{13}(x)}{x^{15}} + \frac{364{x}^{ln(x)}ln^{12}(x)ln^{3}(x)}{x^{15}} + \frac{364{x}^{ln(x)}ln^{4}(x)ln^{11}(x)}{x^{15}} + \frac{1001{x}^{ln(x)}ln^{11}(x)ln^{4}(x)}{x^{15}} + \frac{1001{x}^{ln(x)}ln^{5}(x)ln^{10}(x)}{x^{15}} + \frac{2002{x}^{ln(x)}ln^{10}(x)ln^{5}(x)}{x^{15}} + \frac{2002{x}^{ln(x)}ln^{6}(x)ln^{9}(x)}{x^{15}} + \frac{3003{x}^{ln(x)}ln^{9}(x)ln^{6}(x)}{x^{15}} + \frac{3003{x}^{ln(x)}ln^{7}(x)ln^{8}(x)}{x^{15}} + \frac{3432{x}^{ln(x)}ln^{8}(x)ln^{7}(x)}{x^{15}} + \frac{3432{x}^{ln(x)}ln^{8}(x)ln^{7}(x)}{x^{15}} + \frac{3003{x}^{ln(x)}ln^{7}(x)ln^{8}(x)}{x^{15}} + \frac{3003{x}^{ln(x)}ln^{9}(x)ln^{6}(x)}{x^{15}} + \frac{2002{x}^{ln(x)}ln^{6}(x)ln^{9}(x)}{x^{15}} + \frac{2002{x}^{ln(x)}ln^{10}(x)ln^{5}(x)}{x^{15}} + \frac{1001{x}^{ln(x)}ln^{5}(x)ln^{10}(x)}{x^{15}} + \frac{1001{x}^{ln(x)}ln^{11}(x)ln^{4}(x)}{x^{15}} + \frac{364{x}^{ln(x)}ln^{4}(x)ln^{11}(x)}{x^{15}} + \frac{364{x}^{ln(x)}ln^{12}(x)ln^{3}(x)}{x^{15}} + \frac{91{x}^{ln(x)}ln^{3}(x)ln^{12}(x)}{x^{15}} + \frac{91{x}^{ln(x)}ln^{13}(x)ln^{2}(x)}{x^{15}} + \frac{14{x}^{ln(x)}ln^{2}(x)ln^{13}(x)}{x^{15}} + \frac{14{x}^{ln(x)}ln^{14}(x)ln(x)}{x^{15}} + \frac{{x}^{ln(x)}ln(x)ln^{14}(x)}{x^{15}} + \frac{{x}^{ln(x)}ln(x)ln^{14}(x)}{x^{15}} - \frac{317273316360{x}^{ln(x)}ln^{6}(x)}{x^{15}} - \frac{57492435{x}^{ln(x)}ln^{10}(x)}{x^{15}} - \frac{57492435{x}^{ln(x)}ln^{10}(x)}{x^{15}} + \frac{30655852041744{x}^{ln(x)}ln(x)}{x^{15}} - \frac{6928746825{x}^{ln(x)}ln^{8}(x)}{x^{15}} - \frac{5325948209400{x}^{ln(x)}ln^{4}(x)}{x^{15}} + \frac{3546907{x}^{ln(x)}ln^{11}(x)}{x^{15}} - \frac{6928746825{x}^{ln(x)}ln^{8}(x)}{x^{15}} + \frac{52865397728{x}^{ln(x)}ln^{7}(x)}{x^{15}} + \frac{3546907{x}^{ln(x)}ln^{11}(x)}{x^{15}} - \frac{5325948209400{x}^{ln(x)}ln^{4}(x)}{x^{15}} - \frac{26337645981360{x}^{ln(x)}ln^{2}(x)}{x^{15}} + \frac{14157912634384{x}^{ln(x)}ln^{3}(x)}{x^{15}} - \frac{162435{x}^{ln(x)}ln^{12}(x)}{x^{15}} - \frac{162435{x}^{ln(x)}ln^{12}(x)}{x^{15}} + \frac{714427285{x}^{ln(x)}ln^{9}(x)}{x^{15}} - \frac{317273316360{x}^{ln(x)}ln^{6}(x)}{x^{15}} + \frac{30655852041744{x}^{ln(x)}ln(x)}{x^{15}} + \frac{5215{x}^{ln(x)}ln^{13}(x)}{x^{15}} + \frac{52865397728{x}^{ln(x)}ln^{7}(x)}{x^{15}} + \frac{714427285{x}^{ln(x)}ln^{9}(x)}{x^{15}} + \frac{5215{x}^{ln(x)}ln^{13}(x)}{x^{15}} + \frac{1485309925736{x}^{ln(x)}ln^{5}(x)}{x^{15}} + \frac{1485309925736{x}^{ln(x)}ln^{5}(x)}{x^{15}} - \frac{105{x}^{ln(x)}ln^{14}(x)}{x^{15}} - \frac{105{x}^{ln(x)}ln^{14}(x)}{x^{15}} + \frac{{x}^{ln(x)}ln^{15}(x)}{x^{15}} - \frac{26337645981360{x}^{ln(x)}ln^{2}(x)}{x^{15}} + \frac{14157912634384{x}^{ln(x)}ln^{3}(x)}{x^{15}} + \frac{{x}^{ln(x)}ln^{15}(x)}{x^{15}} - \frac{16828739439120{x}^{ln(x)}}{x^{15}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ {x}^{ln(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&\frac{-26337645981360{x}^{ln(x)}ln(x)ln(x)}{x^{15}} + \frac{24416012857728{x}^{ln(x)}ln^{2}(x)ln(x)}{x^{15}} + \frac{24416012857728{x}^{ln(x)}ln^{2}(x)ln(x)}{x^{15}} - \frac{26337645981360{x}^{ln(x)}ln(x)ln(x)}{x^{15}} - \frac{13639109129100{x}^{ln(x)}ln^{3}(x)ln(x)}{x^{15}} - \frac{15977844628200{x}^{ln(x)}ln^{2}(x)ln^{2}(x)}{x^{15}} + \frac{18057725045424{x}^{ln(x)}ln(x)ln^{2}(x)}{x^{15}} - \frac{15977844628200{x}^{ln(x)}ln^{2}(x)ln^{2}(x)}{x^{15}} - \frac{13639109129100{x}^{ln(x)}ln^{3}(x)ln(x)}{x^{15}} + \frac{18057725045424{x}^{ln(x)}ln(x)ln^{2}(x)}{x^{15}} + \frac{5175704468480{x}^{ln(x)}ln^{4}(x)ln(x)}{x^{15}} + \frac{6451596525920{x}^{ln(x)}ln^{2}(x)ln^{3}(x)}{x^{15}} + \frac{8401502731440{x}^{ln(x)}ln^{3}(x)ln^{2}(x)}{x^{15}} + \frac{8401502731440{x}^{ln(x)}ln^{3}(x)ln^{2}(x)}{x^{15}} - \frac{7664683708500{x}^{ln(x)}ln(x)ln^{3}(x)}{x^{15}} + \frac{6451596525920{x}^{ln(x)}ln^{2}(x)ln^{3}(x)}{x^{15}} + \frac{5175704468480{x}^{ln(x)}ln^{4}(x)ln(x)}{x^{15}} - \frac{7664683708500{x}^{ln(x)}ln(x)ln^{3}(x)}{x^{15}} - \frac{1419567048900{x}^{ln(x)}ln^{5}(x)ln(x)}{x^{15}} - \frac{1794865997925{x}^{ln(x)}ln^{2}(x)ln^{4}(x)}{x^{15}} - \frac{2964233747475{x}^{ln(x)}ln^{4}(x)ln^{2}(x)}{x^{15}} - \frac{3172733163600{x}^{ln(x)}ln^{3}(x)ln^{3}(x)}{x^{15}} + \frac{2250845160200{x}^{ln(x)}ln(x)ln^{4}(x)}{x^{15}} - \frac{3172733163600{x}^{ln(x)}ln^{3}(x)ln^{3}(x)}{x^{15}} - \frac{2964233747475{x}^{ln(x)}ln^{4}(x)ln^{2}(x)}{x^{15}} - \frac{1794865997925{x}^{ln(x)}ln^{2}(x)ln^{4}(x)}{x^{15}} - \frac{1419567048900{x}^{ln(x)}ln^{5}(x)ln(x)}{x^{15}} + \frac{2250845160200{x}^{ln(x)}ln(x)ln^{4}(x)}{x^{15}} + \frac{291353230168{x}^{ln(x)}ln^{6}(x)ln(x)}{x^{15}} + \frac{363702867528{x}^{ln(x)}ln^{2}(x)ln^{5}(x)}{x^{15}} + \frac{746470484760{x}^{ln(x)}ln^{5}(x)ln^{2}(x)}{x^{15}} + \frac{818820122120{x}^{ln(x)}ln^{3}(x)ln^{4}(x)}{x^{15}} - \frac{484072849260{x}^{ln(x)}ln(x)ln^{5}(x)}{x^{15}} + \frac{1031468798360{x}^{ln(x)}ln^{4}(x)ln^{3}(x)}{x^{15}} + \frac{1031468798360{x}^{ln(x)}ln^{4}(x)ln^{3}(x)}{x^{15}} + \frac{818820122120{x}^{ln(x)}ln^{3}(x)ln^{4}(x)}{x^{15}} + \frac{746470484760{x}^{ln(x)}ln^{5}(x)ln^{2}(x)}{x^{15}} + \frac{363702867528{x}^{ln(x)}ln^{2}(x)ln^{5}(x)}{x^{15}} + \frac{291353230168{x}^{ln(x)}ln^{6}(x)ln(x)}{x^{15}} - \frac{484072849260{x}^{ln(x)}ln(x)ln^{5}(x)}{x^{15}} - \frac{45586365825{x}^{ln(x)}ln^{7}(x)ln(x)}{x^{15}} - \frac{55302572325{x}^{ln(x)}ln^{2}(x)ln^{6}(x)}{x^{15}} - \frac{138702338775{x}^{ln(x)}ln^{6}(x)ln^{2}(x)}{x^{15}} - \frac{152305027875{x}^{ln(x)}ln^{3}(x)ln^{5}(x)}{x^{15}} + \frac{78704553928{x}^{ln(x)}ln(x)ln^{6}(x)}{x^{15}} - \frac{235704794325{x}^{ln(x)}ln^{5}(x)ln^{3}(x)}{x^{15}} - \frac{242506138875{x}^{ln(x)}ln^{4}(x)ln^{4}(x)}{x^{15}} - \frac{242506138875{x}^{ln(x)}ln^{4}(x)ln^{4}(x)}{x^{15}} - \frac{235704794325{x}^{ln(x)}ln^{5}(x)ln^{3}(x)}{x^{15}} - \frac{152305027875{x}^{ln(x)}ln^{3}(x)ln^{5}(x)}{x^{15}} - \frac{138702338775{x}^{ln(x)}ln^{6}(x)ln^{2}(x)}{x^{15}} - \frac{55302572325{x}^{ln(x)}ln^{2}(x)ln^{6}(x)}{x^{15}} - \frac{45586365825{x}^{ln(x)}ln^{7}(x)ln(x)}{x^{15}} + \frac{78704553928{x}^{ln(x)}ln(x)ln^{6}(x)}{x^{15}} + \frac{5475848950{x}^{ln(x)}ln^{8}(x)ln(x)}{x^{15}} + \frac{6399902080{x}^{ln(x)}ln^{2}(x)ln^{7}(x)}{x^{15}} + \frac{19319480180{x}^{ln(x)}ln^{7}(x)ln^{2}(x)}{x^{15}} + \frac{20962241300{x}^{ln(x)}ln^{3}(x)ln^{6}(x)}{x^{15}} - \frac{9843608775{x}^{ln(x)}ln(x)ln^{7}(x)}{x^{15}} + \frac{39049650640{x}^{ln(x)}ln^{6}(x)ln^{3}(x)}{x^{15}} + \frac{40487066620{x}^{ln(x)}ln^{4}(x)ln^{5}(x)}{x^{15}} + \frac{49530771290{x}^{ln(x)}ln^{5}(x)ln^{4}(x)}{x^{15}} + \frac{49530771290{x}^{ln(x)}ln^{5}(x)ln^{4}(x)}{x^{15}} + \frac{40487066620{x}^{ln(x)}ln^{4}(x)ln^{5}(x)}{x^{15}} + \frac{39049650640{x}^{ln(x)}ln^{6}(x)ln^{3}(x)}{x^{15}} + \frac{20962241300{x}^{ln(x)}ln^{3}(x)ln^{6}(x)}{x^{15}} + \frac{19319480180{x}^{ln(x)}ln^{7}(x)ln^{2}(x)}{x^{15}} + \frac{6399902080{x}^{ln(x)}ln^{2}(x)ln^{7}(x)}{x^{15}} + \frac{5475848950{x}^{ln(x)}ln^{8}(x)ln(x)}{x^{15}} - \frac{9843608775{x}^{ln(x)}ln(x)ln^{7}(x)}{x^{15}} - \frac{503377875{x}^{ln(x)}ln^{9}(x)ln(x)}{x^{15}} - \frac{564864300{x}^{ln(x)}ln^{2}(x)ln^{8}(x)}{x^{15}} - \frac{2022295275{x}^{ln(x)}ln^{8}(x)ln^{2}(x)}{x^{15}} - \frac{2154051900{x}^{ln(x)}ln^{3}(x)ln^{7}(x)}{x^{15}} + \frac{953996615{x}^{ln(x)}ln(x)ln^{8}(x)}{x^{15}} - \frac{4745040300{x}^{ln(x)}ln^{7}(x)ln^{3}(x)}{x^{15}} - \frac{4903148250{x}^{ln(x)}ln^{4}(x)ln^{6}(x)}{x^{15}} - \frac{7170263100{x}^{ln(x)}ln^{6}(x)ln^{4}(x)}{x^{15}} - \frac{7244046810{x}^{ln(x)}ln^{5}(x)ln^{5}(x)}{x^{15}} - \frac{7244046810{x}^{ln(x)}ln^{5}(x)ln^{5}(x)}{x^{15}} - \frac{7170263100{x}^{ln(x)}ln^{6}(x)ln^{4}(x)}{x^{15}} - \frac{4903148250{x}^{ln(x)}ln^{4}(x)ln^{6}(x)}{x^{15}} - \frac{4745040300{x}^{ln(x)}ln^{7}(x)ln^{3}(x)}{x^{15}} - \frac{2154051900{x}^{ln(x)}ln^{3}(x)ln^{7}(x)}{x^{15}} - \frac{2022295275{x}^{ln(x)}ln^{8}(x)ln^{2}(x)}{x^{15}} + \frac{953996615{x}^{ln(x)}ln(x)ln^{8}(x)}{x^{15}} - \frac{564864300{x}^{ln(x)}ln^{2}(x)ln^{8}(x)}{x^{15}} - \frac{503377875{x}^{ln(x)}ln^{9}(x)ln(x)}{x^{15}} + \frac{34908874{x}^{ln(x)}ln^{10}(x)ln(x)}{x^{15}} + \frac{37647610{x}^{ln(x)}ln^{2}(x)ln^{9}(x)}{x^{15}} + \frac{157432275{x}^{ln(x)}ln^{9}(x)ln^{2}(x)}{x^{15}} + \frac{164279115{x}^{ln(x)}ln^{3}(x)ln^{8}(x)}{x^{15}} - \frac{71546475{x}^{ln(x)}ln(x)ln^{9}(x)}{x^{15}} + \frac{420960540{x}^{ln(x)}ln^{8}(x)ln^{3}(x)}{x^{15}} + \frac{431230800{x}^{ln(x)}ln^{4}(x)ln^{7}(x)}{x^{15}} + \frac{739248510{x}^{ln(x)}ln^{7}(x)ln^{4}(x)}{x^{15}} + \frac{747464718{x}^{ln(x)}ln^{5}(x)ln^{6}(x)}{x^{15}} + \frac{891206316{x}^{ln(x)}ln^{6}(x)ln^{5}(x)}{x^{15}} + \frac{891206316{x}^{ln(x)}ln^{6}(x)ln^{5}(x)}{x^{15}} + \frac{747464718{x}^{ln(x)}ln^{5}(x)ln^{6}(x)}{x^{15}} + \frac{739248510{x}^{ln(x)}ln^{7}(x)ln^{4}(x)}{x^{15}} - \frac{71546475{x}^{ln(x)}ln(x)ln^{9}(x)}{x^{15}} + \frac{431230800{x}^{ln(x)}ln^{4}(x)ln^{7}(x)}{x^{15}} + \frac{420960540{x}^{ln(x)}ln^{8}(x)ln^{3}(x)}{x^{15}} + \frac{164279115{x}^{ln(x)}ln^{3}(x)ln^{8}(x)}{x^{15}} + \frac{157432275{x}^{ln(x)}ln^{9}(x)ln^{2}(x)}{x^{15}} + \frac{37647610{x}^{ln(x)}ln^{2}(x)ln^{9}(x)}{x^{15}} + \frac{34908874{x}^{ln(x)}ln^{10}(x)ln(x)}{x^{15}} - \frac{1773135{x}^{ln(x)}ln^{11}(x)ln(x)}{x^{15}} - \frac{1846845{x}^{ln(x)}ln^{2}(x)ln^{10}(x)}{x^{15}} - \frac{8873865{x}^{ln(x)}ln^{10}(x)ln^{2}(x)}{x^{15}} - \frac{9084075{x}^{ln(x)}ln^{3}(x)ln^{9}(x)}{x^{15}} + \frac{4107103{x}^{ln(x)}ln(x)ln^{10}(x)}{x^{15}} - \frac{26651625{x}^{ln(x)}ln^{9}(x)ln^{3}(x)}{x^{15}} - \frac{27027000{x}^{ln(x)}ln^{4}(x)ln^{8}(x)}{x^{15}} - \frac{53378325{x}^{ln(x)}ln^{8}(x)ln^{4}(x)}{x^{15}} - \frac{53783730{x}^{ln(x)}ln^{5}(x)ln^{7}(x)}{x^{15}} - \frac{74864790{x}^{ln(x)}ln^{7}(x)ln^{5}(x)}{x^{15}} - \frac{75044970{x}^{ln(x)}ln^{6}(x)ln^{6}(x)}{x^{15}} + \frac{4107103{x}^{ln(x)}ln(x)ln^{10}(x)}{x^{15}} - \frac{75044970{x}^{ln(x)}ln^{6}(x)ln^{6}(x)}{x^{15}} - \frac{74864790{x}^{ln(x)}ln^{7}(x)ln^{5}(x)}{x^{15}} - \frac{53783730{x}^{ln(x)}ln^{5}(x)ln^{7}(x)}{x^{15}} - \frac{53378325{x}^{ln(x)}ln^{8}(x)ln^{4}(x)}{x^{15}} - \frac{27027000{x}^{ln(x)}ln^{4}(x)ln^{8}(x)}{x^{15}} - \frac{26651625{x}^{ln(x)}ln^{9}(x)ln^{3}(x)}{x^{15}} - \frac{9084075{x}^{ln(x)}ln^{3}(x)ln^{9}(x)}{x^{15}} - \frac{8873865{x}^{ln(x)}ln^{10}(x)ln^{2}(x)}{x^{15}} - \frac{1846845{x}^{ln(x)}ln^{2}(x)ln^{10}(x)}{x^{15}} - \frac{1773135{x}^{ln(x)}ln^{11}(x)ln(x)}{x^{15}} + \frac{62426{x}^{ln(x)}ln^{12}(x)ln(x)}{x^{15}} + \frac{63336{x}^{ln(x)}ln^{2}(x)ln^{11}(x)}{x^{15}} + \frac{343434{x}^{ln(x)}ln^{11}(x)ln^{2}(x)}{x^{15}} + \frac{346346{x}^{ln(x)}ln^{3}(x)ln^{10}(x)}{x^{15}} - \frac{176085{x}^{ln(x)}ln(x)ln^{11}(x)}{x^{15}} + \frac{1145144{x}^{ln(x)}ln^{10}(x)ln^{3}(x)}{x^{15}} + \frac{1151150{x}^{ln(x)}ln^{4}(x)ln^{9}(x)}{x^{15}} + \frac{2577575{x}^{ln(x)}ln^{9}(x)ln^{4}(x)}{x^{15}} + \frac{2585583{x}^{ln(x)}ln^{5}(x)ln^{8}(x)}{x^{15}} - \frac{176085{x}^{ln(x)}ln(x)ln^{11}(x)}{x^{15}} + \frac{4126122{x}^{ln(x)}ln^{8}(x)ln^{5}(x)}{x^{15}} + \frac{4132128{x}^{ln(x)}ln^{6}(x)ln^{7}(x)}{x^{15}} + \frac{4816812{x}^{ln(x)}ln^{7}(x)ln^{6}(x)}{x^{15}} + \frac{4816812{x}^{ln(x)}ln^{7}(x)ln^{6}(x)}{x^{15}} + \frac{4132128{x}^{ln(x)}ln^{6}(x)ln^{7}(x)}{x^{15}} + \frac{4126122{x}^{ln(x)}ln^{8}(x)ln^{5}(x)}{x^{15}} + \frac{2585583{x}^{ln(x)}ln^{5}(x)ln^{8}(x)}{x^{15}} + \frac{2577575{x}^{ln(x)}ln^{9}(x)ln^{4}(x)}{x^{15}} + \frac{1151150{x}^{ln(x)}ln^{4}(x)ln^{9}(x)}{x^{15}} + \frac{1145144{x}^{ln(x)}ln^{10}(x)ln^{3}(x)}{x^{15}} + \frac{346346{x}^{ln(x)}ln^{3}(x)ln^{10}(x)}{x^{15}} + \frac{343434{x}^{ln(x)}ln^{11}(x)ln^{2}(x)}{x^{15}} + \frac{63336{x}^{ln(x)}ln^{2}(x)ln^{11}(x)}{x^{15}} + \frac{62426{x}^{ln(x)}ln^{12}(x)ln(x)}{x^{15}} - \frac{1365{x}^{ln(x)}ln^{13}(x)ln(x)}{x^{15}} - \frac{1365{x}^{ln(x)}ln^{2}(x)ln^{12}(x)}{x^{15}} - \frac{8190{x}^{ln(x)}ln^{12}(x)ln^{2}(x)}{x^{15}} - \frac{8190{x}^{ln(x)}ln^{3}(x)ln^{11}(x)}{x^{15}} + \frac{5369{x}^{ln(x)}ln(x)ln^{12}(x)}{x^{15}} - \frac{30030{x}^{ln(x)}ln^{11}(x)ln^{3}(x)}{x^{15}} - \frac{30030{x}^{ln(x)}ln^{4}(x)ln^{10}(x)}{x^{15}} + \frac{5369{x}^{ln(x)}ln(x)ln^{12}(x)}{x^{15}} - \frac{75075{x}^{ln(x)}ln^{10}(x)ln^{4}(x)}{x^{15}} - \frac{75075{x}^{ln(x)}ln^{5}(x)ln^{9}(x)}{x^{15}} - \frac{135135{x}^{ln(x)}ln^{9}(x)ln^{5}(x)}{x^{15}} - \frac{135135{x}^{ln(x)}ln^{6}(x)ln^{8}(x)}{x^{15}} - \frac{180180{x}^{ln(x)}ln^{8}(x)ln^{6}(x)}{x^{15}} - \frac{180180{x}^{ln(x)}ln^{7}(x)ln^{7}(x)}{x^{15}} - \frac{180180{x}^{ln(x)}ln^{7}(x)ln^{7}(x)}{x^{15}} - \frac{180180{x}^{ln(x)}ln^{8}(x)ln^{6}(x)}{x^{15}} - \frac{135135{x}^{ln(x)}ln^{6}(x)ln^{8}(x)}{x^{15}} - \frac{135135{x}^{ln(x)}ln^{9}(x)ln^{5}(x)}{x^{15}} - \frac{75075{x}^{ln(x)}ln^{5}(x)ln^{9}(x)}{x^{15}} - \frac{75075{x}^{ln(x)}ln^{10}(x)ln^{4}(x)}{x^{15}} - \frac{30030{x}^{ln(x)}ln^{4}(x)ln^{10}(x)}{x^{15}} - \frac{30030{x}^{ln(x)}ln^{11}(x)ln^{3}(x)}{x^{15}} - \frac{8190{x}^{ln(x)}ln^{3}(x)ln^{11}(x)}{x^{15}} - \frac{8190{x}^{ln(x)}ln^{12}(x)ln^{2}(x)}{x^{15}} - \frac{1365{x}^{ln(x)}ln^{2}(x)ln^{12}(x)}{x^{15}} - \frac{1365{x}^{ln(x)}ln^{13}(x)ln(x)}{x^{15}} + \frac{14{x}^{ln(x)}ln^{14}(x)ln(x)}{x^{15}} + \frac{14{x}^{ln(x)}ln^{2}(x)ln^{13}(x)}{x^{15}} - \frac{105{x}^{ln(x)}ln(x)ln^{13}(x)}{x^{15}} + \frac{91{x}^{ln(x)}ln^{13}(x)ln^{2}(x)}{x^{15}} + \frac{91{x}^{ln(x)}ln^{3}(x)ln^{12}(x)}{x^{15}} - \frac{105{x}^{ln(x)}ln(x)ln^{13}(x)}{x^{15}} + \frac{364{x}^{ln(x)}ln^{12}(x)ln^{3}(x)}{x^{15}} + \frac{364{x}^{ln(x)}ln^{4}(x)ln^{11}(x)}{x^{15}} + \frac{1001{x}^{ln(x)}ln^{11}(x)ln^{4}(x)}{x^{15}} + \frac{1001{x}^{ln(x)}ln^{5}(x)ln^{10}(x)}{x^{15}} + \frac{2002{x}^{ln(x)}ln^{10}(x)ln^{5}(x)}{x^{15}} + \frac{2002{x}^{ln(x)}ln^{6}(x)ln^{9}(x)}{x^{15}} + \frac{3003{x}^{ln(x)}ln^{9}(x)ln^{6}(x)}{x^{15}} + \frac{3003{x}^{ln(x)}ln^{7}(x)ln^{8}(x)}{x^{15}} + \frac{3432{x}^{ln(x)}ln^{8}(x)ln^{7}(x)}{x^{15}} + \frac{3432{x}^{ln(x)}ln^{8}(x)ln^{7}(x)}{x^{15}} + \frac{3003{x}^{ln(x)}ln^{7}(x)ln^{8}(x)}{x^{15}} + \frac{3003{x}^{ln(x)}ln^{9}(x)ln^{6}(x)}{x^{15}} + \frac{2002{x}^{ln(x)}ln^{6}(x)ln^{9}(x)}{x^{15}} + \frac{2002{x}^{ln(x)}ln^{10}(x)ln^{5}(x)}{x^{15}} + \frac{1001{x}^{ln(x)}ln^{5}(x)ln^{10}(x)}{x^{15}} + \frac{1001{x}^{ln(x)}ln^{11}(x)ln^{4}(x)}{x^{15}} + \frac{364{x}^{ln(x)}ln^{4}(x)ln^{11}(x)}{x^{15}} + \frac{364{x}^{ln(x)}ln^{12}(x)ln^{3}(x)}{x^{15}} + \frac{91{x}^{ln(x)}ln^{3}(x)ln^{12}(x)}{x^{15}} + \frac{91{x}^{ln(x)}ln^{13}(x)ln^{2}(x)}{x^{15}} + \frac{14{x}^{ln(x)}ln^{2}(x)ln^{13}(x)}{x^{15}} + \frac{14{x}^{ln(x)}ln^{14}(x)ln(x)}{x^{15}} + \frac{{x}^{ln(x)}ln(x)ln^{14}(x)}{x^{15}} + \frac{{x}^{ln(x)}ln(x)ln^{14}(x)}{x^{15}} - \frac{317273316360{x}^{ln(x)}ln^{6}(x)}{x^{15}} - \frac{57492435{x}^{ln(x)}ln^{10}(x)}{x^{15}} - \frac{57492435{x}^{ln(x)}ln^{10}(x)}{x^{15}} + \frac{30655852041744{x}^{ln(x)}ln(x)}{x^{15}} - \frac{6928746825{x}^{ln(x)}ln^{8}(x)}{x^{15}} - \frac{5325948209400{x}^{ln(x)}ln^{4}(x)}{x^{15}} + \frac{3546907{x}^{ln(x)}ln^{11}(x)}{x^{15}} - \frac{6928746825{x}^{ln(x)}ln^{8}(x)}{x^{15}} + \frac{52865397728{x}^{ln(x)}ln^{7}(x)}{x^{15}} + \frac{3546907{x}^{ln(x)}ln^{11}(x)}{x^{15}} - \frac{5325948209400{x}^{ln(x)}ln^{4}(x)}{x^{15}} - \frac{26337645981360{x}^{ln(x)}ln^{2}(x)}{x^{15}} + \frac{14157912634384{x}^{ln(x)}ln^{3}(x)}{x^{15}} - \frac{162435{x}^{ln(x)}ln^{12}(x)}{x^{15}} - \frac{162435{x}^{ln(x)}ln^{12}(x)}{x^{15}} + \frac{714427285{x}^{ln(x)}ln^{9}(x)}{x^{15}} - \frac{317273316360{x}^{ln(x)}ln^{6}(x)}{x^{15}} + \frac{30655852041744{x}^{ln(x)}ln(x)}{x^{15}} + \frac{5215{x}^{ln(x)}ln^{13}(x)}{x^{15}} + \frac{52865397728{x}^{ln(x)}ln^{7}(x)}{x^{15}} + \frac{714427285{x}^{ln(x)}ln^{9}(x)}{x^{15}} + \frac{5215{x}^{ln(x)}ln^{13}(x)}{x^{15}} + \frac{1485309925736{x}^{ln(x)}ln^{5}(x)}{x^{15}} + \frac{1485309925736{x}^{ln(x)}ln^{5}(x)}{x^{15}} - \frac{105{x}^{ln(x)}ln^{14}(x)}{x^{15}} - \frac{105{x}^{ln(x)}ln^{14}(x)}{x^{15}} + \frac{{x}^{ln(x)}ln^{15}(x)}{x^{15}} - \frac{26337645981360{x}^{ln(x)}ln^{2}(x)}{x^{15}} + \frac{14157912634384{x}^{ln(x)}ln^{3}(x)}{x^{15}} + \frac{{x}^{ln(x)}ln^{15}(x)}{x^{15}} - \frac{16828739439120{x}^{ln(x)}}{x^{15}}\\ \end{split}\end{equation} \]