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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ \frac{{x}^{7}}{sin(x)} + 15x - cos(e^{x} - inx + 3) - tan(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{7}}{sin(x)} + 15x - cos(e^{x} - inx + 3) - tan(x)\\\\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&\frac{1307674368000cos^{8}(x)}{sin^{9}(x)} + \frac{3269185920000cos^{6}(x)}{sin^{7}(x)} + \frac{2713424313600cos^{4}(x)}{sin^{5}(x)} + \frac{796799203200cos^{2}(x)}{sin^{3}(x)} + \frac{44918874000}{sin(x)} - \frac{9153720576000xcos^{9}(x)}{sin^{10}(x)} - \frac{25935541632000xcos^{7}(x)}{sin^{8}(x)} - \frac{25808406624000xcos^{5}(x)}{sin^{6}(x)} - \frac{10300962672000xcos^{3}(x)}{sin^{4}(x)} - \frac{1274402329200xcos(x)}{sin^{2}(x)} + \frac{10035507802320x^{2}cos^{2}(x)}{sin^{3}(x)} + \frac{51073765142400x^{2}cos^{4}(x)}{sin^{5}(x)} + \frac{100919769350400x^{2}cos^{6}(x)}{sin^{7}(x)} + \frac{86960345472000x^{2}cos^{8}(x)}{sin^{9}(x)} + \frac{27461161728000x^{2}cos^{10}(x)}{sin^{11}(x)} - \frac{3098990349000x^{3}cos(x)}{sin^{2}(x)} - \frac{35515391511600x^{3}cos^{3}(x)}{sin^{4}(x)} + \frac{9395346269400x^{4}cos^{2}(x)}{sin^{3}(x)} - \frac{130437491184000x^{3}cos^{5}(x)}{sin^{6}(x)} + \frac{66187418497200x^{4}cos^{4}(x)}{sin^{5}(x)} - \frac{212442598368000x^{3}cos^{7}(x)}{sin^{8}(x)} + \frac{189143594640000x^{4}cos^{6}(x)}{sin^{7}(x)} - \frac{879181926210x^{5}cos(x)}{sin^{2}(x)} - \frac{160190110080000x^{3}cos^{9}(x)}{sin^{10}(x)} - \frac{13520109821400x^{5}cos^{3}(x)}{sin^{4}(x)} + \frac{1007587936110x^{6}cos^{2}(x)}{sin^{3}(x)} + \frac{261770981472000x^{4}cos^{8}(x)}{sin^{9}(x)} - \frac{67652245861200x^{5}cos^{5}(x)}{sin^{6}(x)} + \frac{9341468299800x^{6}cos^{4}(x)}{sin^{5}(x)} - \frac{19391512145x^{7}cos(x)}{sin^{2}(x)} - \frac{45768602880000x^{3}cos^{11}(x)}{sin^{12}(x)} - \frac{157761831427200x^{5}cos^{7}(x)}{sin^{8}(x)} - \frac{384653685786x^{7}cos^{3}(x)}{sin^{4}(x)} + \frac{35958245122800x^{6}cos^{6}(x)}{sin^{7}(x)} - \frac{2499588687960x^{7}cos^{5}(x)}{sin^{6}(x)} + \frac{175446311040000x^{4}cos^{10}(x)}{sin^{11}(x)} - \frac{189710858937600x^{5}cos^{9}(x)}{sin^{10}(x)} - \frac{7784050594320x^{7}cos^{7}(x)}{sin^{8}(x)} + \frac{70702199568000x^{6}cos^{8}(x)}{sin^{9}(x)} + \frac{45768602880000x^{4}cos^{12}(x)}{sin^{13}(x)} - \frac{13216073270400x^{7}cos^{9}(x)}{sin^{10}(x)} + \frac{75136789728000x^{6}cos^{10}(x)}{sin^{11}(x)} - \frac{12579100934400x^{7}cos^{11}(x)}{sin^{12}(x)} - \frac{114421507200000x^{5}cos^{11}(x)}{sin^{12}(x)} + \frac{41191742592000x^{6}cos^{12}(x)}{sin^{13}(x)} - \frac{6320426112000x^{7}cos^{13}(x)}{sin^{14}(x)} - \frac{27461161728000x^{5}cos^{13}(x)}{sin^{14}(x)} + \frac{9153720576000x^{6}cos^{14}(x)}{sin^{15}(x)} - \frac{1307674368000x^{7}cos^{15}(x)}{sin^{16}(x)} + \frac{20932903005x^{6}}{sin(x)} + \frac{258249195750x^{4}}{sin(x)} + \frac{382320698760x^{2}}{sin(x)} + e^{x}sin(e^{x} - inx + 3) + 16383e^{{x}*{2}}cos(e^{x} - inx + 3) - 15ine^{x}cos(e^{x} - inx + 3) - 2375101e^{{x}*{3}}sin(e^{x} - inx + 3) + 122865ine^{{x}*{2}}sin(e^{x} - inx + 3) - 105i^{2}n^{2}e^{x}sin(e^{x} - inx + 3) - 42355950e^{{x}*{4}}cos(e^{x} - inx + 3) + 11834550ine^{{x}*{3}}cos(e^{x} - inx + 3) - 429975i^{2}n^{2}e^{{x}*{2}}cos(e^{x} - inx + 3) + 455i^{3}n^{3}e^{x}cos(e^{x} - inx + 3) + 210766920e^{{x}*{5}}sin(e^{x} - inx + 3) - 155876175ine^{{x}*{4}}sin(e^{x} - inx + 3) + 27470625i^{2}n^{2}e^{{x}*{3}}sin(e^{x} - inx + 3) - 931385i^{3}n^{3}e^{{x}*{2}}sin(e^{x} - inx + 3) + 1365i^{4}n^{4}e^{x}sin(e^{x} - inx + 3) + 420693273e^{{x}*{6}}cos(e^{x} - inx + 3) - 601125525ine^{{x}*{5}}cos(e^{x} - inx + 3) + 265915650i^{2}n^{2}e^{{x}*{4}}cos(e^{x} - inx + 3) - 39369330i^{3}n^{3}e^{{x}*{3}}cos(e^{x} - inx + 3) + 1396395i^{4}n^{4}e^{{x}*{2}}cos(e^{x} - inx + 3) - 3003i^{5}n^{5}e^{x}cos(e^{x} - inx + 3) - 408741333e^{{x}*{7}}sin(e^{x} - inx + 3) + 951545595ine^{{x}*{6}}sin(e^{x} - inx + 3) - 788392605i^{2}n^{2}e^{{x}*{5}}sin(e^{x} - inx + 3) + 278232955i^{3}n^{3}e^{{x}*{4}}sin(e^{x} - inx + 3) - 38903865i^{4}n^{4}e^{{x}*{3}}sin(e^{x} - inx + 3) + 1534533i^{5}n^{5}e^{{x}*{2}}sin(e^{x} - inx + 3) - 5005i^{6}n^{6}e^{x}sin(e^{x} - inx + 3) - 216627840e^{{x}*{8}}cos(e^{x} - inx + 3) + 739939200ine^{{x}*{7}}cos(e^{x} - inx + 3) - 978737760i^{2}n^{2}e^{{x}*{6}}cos(e^{x} - inx + 3) + 627627000i^{3}n^{3}e^{{x}*{5}}cos(e^{x} - inx + 3) - 198948750i^{4}n^{4}e^{{x}*{4}}cos(e^{x} - inx + 3) + 28017990i^{5}n^{5}e^{{x}*{3}}cos(e^{x} - inx + 3) - 1276275i^{6}n^{6}e^{{x}*{2}}cos(e^{x} - inx + 3) + 6435i^{7}n^{7}e^{x}cos(e^{x} - inx + 3) + 67128490e^{{x}*{9}}sin(e^{x} - inx + 3) - 313684800ine^{{x}*{8}}sin(e^{x} - inx + 3) + 600119520i^{2}n^{2}e^{{x}*{7}}sin(e^{x} - inx + 3) - 602261660i^{3}n^{3}e^{{x}*{6}}sin(e^{x} - inx + 3) + 336786450i^{4}n^{4}e^{{x}*{5}}sin(e^{x} - inx + 3) - 102417315i^{5}n^{5}e^{{x}*{4}}sin(e^{x} - inx + 3) + 15140125i^{6}n^{6}e^{{x}*{3}}sin(e^{x} - inx + 3) - 817245i^{7}n^{7}e^{{x}*{2}}sin(e^{x} - inx + 3) + 6435i^{8}n^{8}e^{x}sin(e^{x} - inx + 3) + 12662650e^{{x}*{10}}cos(e^{x} - inx + 3) - 77026950ine^{{x}*{9}}cos(e^{x} - inx + 3) + 199459260i^{2}n^{2}e^{{x}*{8}}cos(e^{x} - inx + 3) - 285465180i^{3}n^{3}e^{{x}*{7}}cos(e^{x} - inx + 3) + 244999755i^{4}n^{4}e^{{x}*{6}}cos(e^{x} - inx + 3) - 127702575i^{5}n^{5}e^{{x}*{5}}cos(e^{x} - inx + 3) + 38888850i^{6}n^{6}e^{{x}*{4}}cos(e^{x} - inx + 3) - 6216210i^{7}n^{7}e^{{x}*{3}}cos(e^{x} - inx + 3) + 405405i^{8}n^{8}e^{{x}*{2}}cos(e^{x} - inx + 3) - 5005i^{9}n^{9}e^{x}cos(e^{x} - inx + 3) - 1479478e^{{x}*{11}}sin(e^{x} - inx + 3) + 11291280ine^{{x}*{10}}sin(e^{x} - inx + 3) - 37747710i^{2}n^{2}e^{{x}*{9}}sin(e^{x} - inx + 3) + 72357285i^{3}n^{3}e^{{x}*{8}}sin(e^{x} - inx + 3) - 87342255i^{4}n^{4}e^{{x}*{7}}sin(e^{x} - inx + 3) + 68549481i^{5}n^{5}e^{{x}*{6}}sin(e^{x} - inx + 3) - 34789755i^{6}n^{6}e^{{x}*{5}}sin(e^{x} - inx + 3) + 10945935i^{7}n^{7}e^{{x}*{4}}sin(e^{x} - inx + 3) - 1936935i^{8}n^{8}e^{{x}*{3}}sin(e^{x} - inx + 3) + 155155i^{9}n^{9}e^{{x}*{2}}sin(e^{x} - inx + 3) - 3003i^{10}n^{10}e^{x}sin(e^{x} - inx + 3) - 106470e^{{x}*{12}}cos(e^{x} - inx + 3) + 990990ine^{{x}*{11}}cos(e^{x} - inx + 3) - 4129125i^{2}n^{2}e^{{x}*{10}}cos(e^{x} - inx + 3) + 10135125i^{3}n^{3}e^{{x}*{9}}cos(e^{x} - inx + 3) - 16216200i^{4}n^{4}e^{{x}*{8}}cos(e^{x} - inx + 3) + 17657640i^{5}n^{5}e^{{x}*{7}}cos(e^{x} - inx + 3) - 13243230i^{6}n^{6}e^{{x}*{6}}cos(e^{x} - inx + 3) + 6756750i^{7}n^{7}e^{{x}*{5}}cos(e^{x} - inx + 3) - 2252250i^{8}n^{8}e^{{x}*{4}}cos(e^{x} - inx + 3) + 450450i^{9}n^{9}e^{{x}*{3}}cos(e^{x} - inx + 3) - 45045i^{10}n^{10}e^{{x}*{2}}cos(e^{x} - inx + 3) + 1365i^{11}n^{11}e^{x}cos(e^{x} - inx + 3) + 4550e^{{x}*{13}}sin(e^{x} - inx + 3) - 50505ine^{{x}*{12}}sin(e^{x} - inx + 3) + 255255i^{2}n^{2}e^{{x}*{11}}sin(e^{x} - inx + 3) - 775775i^{3}n^{3}e^{{x}*{10}}sin(e^{x} - inx + 3) + 1576575i^{4}n^{4}e^{{x}*{9}}sin(e^{x} - inx + 3) - 2252250i^{5}n^{5}e^{{x}*{8}}sin(e^{x} - inx + 3) + 2312310i^{6}n^{6}e^{{x}*{7}}sin(e^{x} - inx + 3) - 1711710i^{7}n^{7}e^{{x}*{6}}sin(e^{x} - inx + 3) + 900900i^{8}n^{8}e^{{x}*{5}}sin(e^{x} - inx + 3) - 325325i^{9}n^{9}e^{{x}*{4}}sin(e^{x} - inx + 3) + 75075i^{10}n^{10}e^{{x}*{3}}sin(e^{x} - inx + 3) - 9555i^{11}n^{11}e^{{x}*{2}}sin(e^{x} - inx + 3) + 455i^{12}n^{12}e^{x}sin(e^{x} - inx + 3) + 105e^{{x}*{14}}cos(e^{x} - inx + 3) - 1365ine^{{x}*{13}}cos(e^{x} - inx + 3) + 8190i^{2}n^{2}e^{{x}*{12}}cos(e^{x} - inx + 3) - 30030i^{3}n^{3}e^{{x}*{11}}cos(e^{x} - inx + 3) + 75075i^{4}n^{4}e^{{x}*{10}}cos(e^{x} - inx + 3) - 135135i^{5}n^{5}e^{{x}*{9}}cos(e^{x} - inx + 3) + 180180i^{6}n^{6}e^{{x}*{8}}cos(e^{x} - inx + 3) - 180180i^{7}n^{7}e^{{x}*{7}}cos(e^{x} - inx + 3) + 135135i^{8}n^{8}e^{{x}*{6}}cos(e^{x} - inx + 3) - 75075i^{9}n^{9}e^{{x}*{5}}cos(e^{x} - inx + 3) + 30030i^{10}n^{10}e^{{x}*{4}}cos(e^{x} - inx + 3) - 8190i^{11}n^{11}e^{{x}*{3}}cos(e^{x} - inx + 3) + 1365i^{12}n^{12}e^{{x}*{2}}cos(e^{x} - inx + 3) - 105i^{13}n^{13}e^{x}cos(e^{x} - inx + 3) - e^{{x}*{15}}sin(e^{x} - inx + 3) + 15ine^{{x}*{14}}sin(e^{x} - inx + 3) - 105i^{2}n^{2}e^{{x}*{13}}sin(e^{x} - inx + 3) + 455i^{3}n^{3}e^{{x}*{12}}sin(e^{x} - inx + 3) - 1365i^{4}n^{4}e^{{x}*{11}}sin(e^{x} - inx + 3) + 3003i^{5}n^{5}e^{{x}*{10}}sin(e^{x} - inx + 3) - 5005i^{6}n^{6}e^{{x}*{9}}sin(e^{x} - inx + 3) + 6435i^{7}n^{7}e^{{x}*{8}}sin(e^{x} - inx + 3) - 6435i^{8}n^{8}e^{{x}*{7}}sin(e^{x} - inx + 3) + 5005i^{9}n^{9}e^{{x}*{6}}sin(e^{x} - inx + 3) - 3003i^{10}n^{10}e^{{x}*{5}}sin(e^{x} - inx + 3) + 1365i^{11}n^{11}e^{{x}*{4}}sin(e^{x} - inx + 3) - 455i^{12}n^{12}e^{{x}*{3}}sin(e^{x} - inx + 3) + 105i^{13}n^{13}e^{{x}*{2}}sin(e^{x} - inx + 3) - 15i^{14}n^{14}e^{x}sin(e^{x} - inx + 3) + i^{15}n^{15}sin(e^{x} - inx + 3) - 1903757312sec^{16}(x) - 89702612992tan^{2}(x)sec^{14}(x) - 460858269696tan^{4}(x)sec^{12}(x) - 559148810240tan^{6}(x)sec^{10}(x) - 182172651520tan^{8}(x)sec^{8}(x) - 13754155008tan^{10}(x)sec^{6}(x) - 134094848tan^{12}(x)sec^{4}(x) - 16384tan^{14}(x)sec^{2}(x)\\ \end{split}\end{equation} \]