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 7 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 7th\ derivative\ of\ function\ \frac{(sin(x) + 6{x}^{3} + 5{x}^{4})}{(cos(x) + x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{sin(x)}{(cos(x) + x)} + \frac{6x^{3}}{(cos(x) + x)} + \frac{5x^{4}}{(cos(x) + x)}\\\\ &\color{blue}{The\ 7th\ derivative\ of\ function:} \\=&\frac{20160sin^{6}(x)cos(x)}{(cos(x) + x)^{7}} - \frac{105840sin^{5}(x)cos(x)}{(cos(x) + x)^{7}} + \frac{25200sin^{4}(x)cos^{2}(x)}{(cos(x) + x)^{6}} - \frac{15120sin^{4}(x)cos(x)}{(cos(x) + x)^{5}} + \frac{226800sin^{4}(x)cos(x)}{(cos(x) + x)^{7}} - \frac{88200sin^{3}(x)cos^{2}(x)}{(cos(x) + x)^{6}} + \frac{41160sin^{3}(x)cos(x)}{(cos(x) + x)^{5}} + \frac{10080sin^{2}(x)cos^{3}(x)}{(cos(x) + x)^{5}} - \frac{7560sin^{2}(x)cos^{2}(x)}{(cos(x) + x)^{4}} - \frac{37800sin^{2}(x)cos(x)}{(cos(x) + x)^{5}} - \frac{252000sin^{3}(x)cos(x)}{(cos(x) + x)^{7}} + \frac{113400sin^{2}(x)cos^{2}(x)}{(cos(x) + x)^{6}} + \frac{1512sin^{2}(x)cos(x)}{(cos(x) + x)^{3}} - \frac{17640sin(x)cos^{3}(x)}{(cos(x) + x)^{5}} - \frac{63000sin(x)cos^{2}(x)}{(cos(x) + x)^{6}} + \frac{8820sin(x)cos^{2}(x)}{(cos(x) + x)^{4}} + \frac{45360sin^{2}(x)cos(x)}{(cos(x) + x)^{4}} + \frac{630cos^{4}(x)}{(cos(x) + x)^{4}} + \frac{7560cos^{3}(x)}{(cos(x) + x)^{5}} - \frac{90720sin(x)cos(x)}{(cos(x) + x)^{4}} - \frac{420cos^{3}(x)}{(cos(x) + x)^{3}} + \frac{7560cos^{2}(x)}{(cos(x) + x)^{3}} + \frac{24318sin(x)cos(x)}{(cos(x) + x)^{3}} + \frac{151200sin^{2}(x)cos(x)}{(cos(x) + x)^{7}} - \frac{45360sin(x)cos(x)}{(cos(x) + x)^{7}} + \frac{12600cos^{2}(x)}{(cos(x) + x)^{6}} + \frac{12600sin(x)cos(x)}{(cos(x) + x)^{5}} - \frac{1890cos^{2}(x)}{(cos(x) + x)^{4}} - \frac{73584sin^{2}(x)}{(cos(x) + x)^{4}} + \frac{63cos^{2}(x)}{(cos(x) + x)^{2}} - \frac{64sin^{2}(x)}{(cos(x) + x)^{2}} - \frac{6720sin^{6}(x)}{(cos(x) + x)^{6}} + \frac{42000sin^{3}(x)}{(cos(x) + x)^{6}} - \frac{50400sin^{4}(x)}{(cos(x) + x)^{6}} + \frac{29400sin^{5}(x)}{(cos(x) + x)^{6}} - \frac{35280sin^{7}(x)}{(cos(x) + x)^{8}} + \frac{5040sin^{8}(x)}{(cos(x) + x)^{8}} - \frac{10080sin^{2}(x)}{(cos(x) + x)^{3}} + \frac{21378sin^{3}(x)}{(cos(x) + x)^{4}} + \frac{2016sin^{4}(x)}{(cos(x) + x)^{4}} + \frac{105840sin^{6}(x)}{(cos(x) + x)^{8}} - \frac{176400sin^{5}(x)}{(cos(x) + x)^{8}} + \frac{176400sin^{4}(x)}{(cos(x) + x)^{8}} - \frac{105840sin^{3}(x)}{(cos(x) + x)^{8}} + \frac{35280sin^{2}(x)}{(cos(x) + x)^{8}} - \frac{16800sin^{2}(x)}{(cos(x) + x)^{6}} - \frac{5040sin(x)}{(cos(x) + x)^{8}} + \frac{5040cos(x)}{(cos(x) + x)^{7}} + \frac{2520sin(x)}{(cos(x) + x)^{6}} - \frac{840cos(x)}{(cos(x) + x)^{5}} + \frac{75390sin(x)}{(cos(x) + x)^{4}} - \frac{25158cos(x)}{(cos(x) + x)^{3}} - \frac{4193sin(x)}{(cos(x) + x)^{2}} - \frac{cos(x)}{(cos(x) + x)} + \frac{90720x^{3}sin^{5}(x)cos(x)}{(cos(x) + x)^{7}} - \frac{453600x^{3}sin^{4}(x)cos(x)}{(cos(x) + x)^{7}} + \frac{226800x^{2}sin^{4}(x)cos(x)}{(cos(x) + x)^{6}} + \frac{75600x^{3}sin^{3}(x)cos^{2}(x)}{(cos(x) + x)^{6}} - \frac{35280x^{3}sin^{3}(x)cos(x)}{(cos(x) + x)^{5}} + \frac{907200x^{3}sin^{3}(x)cos(x)}{(cos(x) + x)^{7}} - \frac{907200x^{2}sin^{3}(x)cos(x)}{(cos(x) + x)^{6}} - \frac{226800x^{3}sin^{2}(x)cos^{2}(x)}{(cos(x) + x)^{6}} + \frac{75600x^{3}sin^{2}(x)cos(x)}{(cos(x) + x)^{5}} + \frac{181440xsin^{3}(x)cos(x)}{(cos(x) + x)^{5}} + \frac{136080x^{2}sin^{2}(x)cos^{2}(x)}{(cos(x) + x)^{5}} - \frac{56700x^{2}sin^{2}(x)cos(x)}{(cos(x) + x)^{4}} + \frac{15120x^{3}sin(x)cos^{3}(x)}{(cos(x) + x)^{5}} - \frac{63000x^{3}sin^{2}(x)cos(x)}{(cos(x) + x)^{4}} - \frac{7560x^{3}sin(x)cos^{2}(x)}{(cos(x) + x)^{4}} - \frac{29400x^{4}sin^{3}(x)cos(x)}{(cos(x) + x)^{5}} - \frac{907200x^{3}sin^{2}(x)cos(x)}{(cos(x) + x)^{7}} + \frac{1360800x^{2}sin^{2}(x)cos(x)}{(cos(x) + x)^{6}} + \frac{226800x^{3}sin(x)cos^{2}(x)}{(cos(x) + x)^{6}} + \frac{63000x^{4}sin^{2}(x)cos(x)}{(cos(x) + x)^{5}} - \frac{544320xsin^{2}(x)cos(x)}{(cos(x) + x)^{5}} - \frac{272160x^{2}sin(x)cos^{2}(x)}{(cos(x) + x)^{5}} + \frac{544320xsin(x)cos(x)}{(cos(x) + x)^{5}} - \frac{15120x^{3}cos^{3}(x)}{(cos(x) + x)^{5}} - \frac{907200x^{2}sin(x)cos(x)}{(cos(x) + x)^{6}} - \frac{6300x^{4}sin(x)cos^{2}(x)}{(cos(x) + x)^{4}} + \frac{68040xsin(x)cos^{2}(x)}{(cos(x) + x)^{4}} + \frac{113400x^{2}sin(x)cos^{2}(x)}{(cos(x) + x)^{4}} + \frac{151200xsin^{2}(x)cos(x)}{(cos(x) + x)^{4}} + \frac{11340x^{2}cos^{3}(x)}{(cos(x) + x)^{4}} + \frac{12600x^{4}sin(x)cos^{3}(x)}{(cos(x) + x)^{5}} - \frac{68040xcos^{2}(x)}{(cos(x) + x)^{4}} - \frac{302400xsin(x)cos(x)}{(cos(x) + x)^{4}} + \frac{136080x^{2}cos^{2}(x)}{(cos(x) + x)^{5}} + \frac{68040x^{2}sin(x)cos(x)}{(cos(x) + x)^{4}} + \frac{151200x^{3}sin^{2}(x)cos^{2}(x)}{(cos(x) + x)^{5}} + \frac{12600x^{3}cos^{3}(x)}{(cos(x) + x)^{4}} - \frac{302400x^{3}sin(x)cos^{2}(x)}{(cos(x) + x)^{5}} - \frac{75600x^{3}cos^{2}(x)}{(cos(x) + x)^{6}} + \frac{63000x^{4}sin^{3}(x)cos^{2}(x)}{(cos(x) + x)^{6}} - \frac{12600x^{4}cos^{3}(x)}{(cos(x) + x)^{5}} + \frac{302400x^{2}sin^{3}(x)cos(x)}{(cos(x) + x)^{5}} - \frac{907200x^{2}sin^{2}(x)cos(x)}{(cos(x) + x)^{5}} + \frac{75600x^{3}sin(x)cos(x)}{(cos(x) + x)^{4}} + \frac{453600x^{3}sin(x)cos(x)}{(cos(x) + x)^{7}} - \frac{189000x^{4}sin^{2}(x)cos^{2}(x)}{(cos(x) + x)^{6}} + \frac{189000x^{4}sin(x)cos^{2}(x)}{(cos(x) + x)^{6}} - \frac{113400x^{2}cos^{2}(x)}{(cos(x) + x)^{4}} + \frac{907200x^{2}sin(x)cos(x)}{(cos(x) + x)^{5}} + \frac{252000x^{3}sin^{4}(x)cos(x)}{(cos(x) + x)^{6}} - \frac{1008000x^{3}sin^{3}(x)cos(x)}{(cos(x) + x)^{6}} + \frac{3150x^{4}cos^{2}(x)}{(cos(x) + x)^{4}} + \frac{1512000x^{3}sin^{2}(x)cos(x)}{(cos(x) + x)^{6}} + \frac{3780x^{3}cos^{2}(x)}{(cos(x) + x)^{4}} - \frac{45360x^{3}sin(x)cos(x)}{(cos(x) + x)^{5}} - \frac{1008000x^{3}sin(x)cos(x)}{(cos(x) + x)^{6}} + \frac{25200xcos^{2}(x)}{(cos(x) + x)^{3}} - \frac{37800x^{4}sin(x)cos(x)}{(cos(x) + x)^{5}} + \frac{151200x^{3}cos^{2}(x)}{(cos(x) + x)^{5}} - \frac{22680xsin(x)cos(x)}{(cos(x) + x)^{3}} - \frac{37800x^{2}sin(x)cos(x)}{(cos(x) + x)^{3}} + \frac{756x^{3}sin(x)cos(x)}{(cos(x) + x)^{3}} + \frac{630x^{4}sin(x)cos(x)}{(cos(x) + x)^{3}} + \frac{75600x^{4}sin^{5}(x)cos(x)}{(cos(x) + x)^{7}} - \frac{378000x^{4}sin^{4}(x)cos(x)}{(cos(x) + x)^{7}} + \frac{756000x^{4}sin^{3}(x)cos(x)}{(cos(x) + x)^{7}} - \frac{756000x^{4}sin^{2}(x)cos(x)}{(cos(x) + x)^{7}} + \frac{378000x^{4}sin(x)cos(x)}{(cos(x) + x)^{7}} - \frac{4200x^{3}cos^{2}(x)}{(cos(x) + x)^{3}} - \frac{3360x^{4}sin^{2}(x)}{(cos(x) + x)^{4}} - \frac{3780x^{2}cos^{2}(x)}{(cos(x) + x)^{3}} - \frac{4032x^{3}sin^{2}(x)}{(cos(x) + x)^{4}} - \frac{63000x^{4}cos^{2}(x)}{(cos(x) + x)^{6}} + \frac{3276x^{3}sin^{3}(x)}{(cos(x) + x)^{4}} + \frac{90720xsin^{2}(x)}{(cos(x) + x)^{4}} - \frac{181440x^{2}sin^{2}(x)}{(cos(x) + x)^{5}} - \frac{201600x^{3}sin^{2}(x)}{(cos(x) + x)^{5}} + \frac{151200x^{2}sin^{2}(x)}{(cos(x) + x)^{4}} - \frac{33600xsin^{2}(x)}{(cos(x) + x)^{3}} + \frac{4032x^{2}sin^{2}(x)}{(cos(x) + x)^{3}} + \frac{4480x^{3}sin^{2}(x)}{(cos(x) + x)^{3}} - \frac{75600x^{2}sin^{3}(x)}{(cos(x) + x)^{4}} + \frac{181440x^{2}sin^{3}(x)}{(cos(x) + x)^{5}} - \frac{60480x^{2}sin^{4}(x)}{(cos(x) + x)^{5}} + \frac{2730x^{4}sin^{3}(x)}{(cos(x) + x)^{4}} - \frac{67200x^{3}sin^{4}(x)}{(cos(x) + x)^{5}} + \frac{201600x^{3}sin^{3}(x)}{(cos(x) + x)^{5}} - \frac{45360xsin^{3}(x)}{(cos(x) + x)^{4}} + \frac{100800x^{3}sin^{4}(x)}{(cos(x) + x)^{6}} - \frac{21000x^{4}sin^{5}(x)}{(cos(x) + x)^{6}} + \frac{100800xsin^{4}(x)}{(cos(x) + x)^{5}} - \frac{403200xsin^{3}(x)}{(cos(x) + x)^{5}} - \frac{25200x^{3}sin^{5}(x)}{(cos(x) + x)^{6}} + \frac{84000x^{4}sin^{4}(x)}{(cos(x) + x)^{6}} - \frac{151200x^{3}sin^{3}(x)}{(cos(x) + x)^{6}} - \frac{126000x^{4}sin^{3}(x)}{(cos(x) + x)^{6}} + \frac{151200x^{2}sin^{5}(x)}{(cos(x) + x)^{6}} + \frac{90720xsin^{5}(x)}{(cos(x) + x)^{6}} - \frac{453600xsin^{4}(x)}{(cos(x) + x)^{6}} - \frac{756000x^{2}sin^{4}(x)}{(cos(x) + x)^{6}} + \frac{907200xsin^{3}(x)}{(cos(x) + x)^{6}} + \frac{1512000x^{2}sin^{3}(x)}{(cos(x) + x)^{6}} + \frac{30240x^{3}sin^{7}(x)}{(cos(x) + x)^{8}} + \frac{25200x^{4}sin^{7}(x)}{(cos(x) + x)^{8}} - \frac{211680x^{3}sin^{6}(x)}{(cos(x) + x)^{8}} - \frac{176400x^{4}sin^{6}(x)}{(cos(x) + x)^{8}} + \frac{30240sin^{4}(x)}{(cos(x) + x)^{5}} + \frac{635040x^{3}sin^{5}(x)}{(cos(x) + x)^{8}} + \frac{529200x^{4}sin^{5}(x)}{(cos(x) + x)^{8}} - \frac{120960sin^{3}(x)}{(cos(x) + x)^{5}} - \frac{1058400x^{3}sin^{4}(x)}{(cos(x) + x)^{8}} - \frac{882000x^{4}sin^{4}(x)}{(cos(x) + x)^{8}} + \frac{604800xsin^{2}(x)}{(cos(x) + x)^{5}} - \frac{604800x^{3}sin^{5}(x)}{(cos(x) + x)^{7}} + \frac{90720x^{2}sin^{6}(x)}{(cos(x) + x)^{7}} + \frac{181440sin^{2}(x)}{(cos(x) + x)^{5}} + \frac{1360800x^{2}sin^{4}(x)}{(cos(x) + x)^{7}} - \frac{544320x^{2}sin^{5}(x)}{(cos(x) + x)^{7}} + \frac{1512000x^{3}sin^{4}(x)}{(cos(x) + x)^{7}} + \frac{100800x^{3}sin^{6}(x)}{(cos(x) + x)^{7}} - \frac{1814400x^{2}sin^{3}(x)}{(cos(x) + x)^{7}} + \frac{1058400x^{3}sin^{3}(x)}{(cos(x) + x)^{8}} - \frac{2016000x^{3}sin^{3}(x)}{(cos(x) + x)^{7}} + \frac{882000x^{4}sin^{3}(x)}{(cos(x) + x)^{8}} + \frac{100800x^{3}sin^{2}(x)}{(cos(x) + x)^{6}} - \frac{635040x^{3}sin^{2}(x)}{(cos(x) + x)^{8}} + \frac{1360800x^{2}sin^{2}(x)}{(cos(x) + x)^{7}} - \frac{907200xsin^{2}(x)}{(cos(x) + x)^{6}} - \frac{529200x^{4}sin^{2}(x)}{(cos(x) + x)^{8}} + \frac{1512000x^{3}sin^{2}(x)}{(cos(x) + x)^{7}} - \frac{1512000x^{2}sin^{2}(x)}{(cos(x) + x)^{6}} + \frac{84000x^{4}sin^{2}(x)}{(cos(x) + x)^{6}} - \frac{120960sin(x)}{(cos(x) + x)^{5}} + \frac{45360cos(x)}{(cos(x) + x)^{4}} + \frac{10080sin(x)}{(cos(x) + x)^{3}} - \frac{1260cos(x)}{(cos(x) + x)^{2}} - \frac{181440xcos(x)}{(cos(x) + x)^{5}} - \frac{45360xsin(x)}{(cos(x) + x)^{4}} + \frac{7560xcos(x)}{(cos(x) + x)^{3}} + \frac{756xsin(x)}{(cos(x) + x)^{2}} + \frac{226800x^{2}cos(x)}{(cos(x) + x)^{6}} + \frac{60480x^{2}sin(x)}{(cos(x) + x)^{5}} - \frac{11340x^{2}cos(x)}{(cos(x) + x)^{4}} - \frac{1512x^{2}sin(x)}{(cos(x) + x)^{3}} + \frac{126x^{2}cos(x)}{(cos(x) + x)^{2}} - \frac{90720x^{3}cos(x)}{(cos(x) + x)^{7}} - \frac{25200x^{3}sin(x)}{(cos(x) + x)^{6}} + \frac{5040x^{3}cos(x)}{(cos(x) + x)^{5}} + \frac{756x^{3}sin(x)}{(cos(x) + x)^{4}} - \frac{84x^{3}cos(x)}{(cos(x) + x)^{3}} - \frac{6x^{3}sin(x)}{(cos(x) + x)^{2}} + \frac{211680x^{3}sin(x)}{(cos(x) + x)^{8}} - \frac{544320x^{2}sin(x)}{(cos(x) + x)^{7}} + \frac{453600xsin(x)}{(cos(x) + x)^{6}} + \frac{176400x^{4}sin(x)}{(cos(x) + x)^{8}} - \frac{604800x^{3}sin(x)}{(cos(x) + x)^{7}} - \frac{75600x^{4}cos(x)}{(cos(x) + x)^{7}} + \frac{756000x^{2}sin(x)}{(cos(x) + x)^{6}} + \frac{252000x^{3}cos(x)}{(cos(x) + x)^{6}} - \frac{21000x^{4}sin(x)}{(cos(x) + x)^{6}} - \frac{403200xsin(x)}{(cos(x) + x)^{5}} - \frac{302400x^{2}cos(x)}{(cos(x) + x)^{5}} + \frac{67200x^{3}sin(x)}{(cos(x) + x)^{5}} + \frac{4200x^{4}cos(x)}{(cos(x) + x)^{5}} + \frac{151200xcos(x)}{(cos(x) + x)^{4}} - \frac{75600x^{2}sin(x)}{(cos(x) + x)^{4}} - \frac{12600x^{3}cos(x)}{(cos(x) + x)^{4}} + \frac{630x^{4}sin(x)}{(cos(x) + x)^{4}} + \frac{33600xsin(x)}{(cos(x) + x)^{3}} + \frac{12600x^{2}cos(x)}{(cos(x) + x)^{3}} - \frac{1680x^{3}sin(x)}{(cos(x) + x)^{3}} - \frac{70x^{4}cos(x)}{(cos(x) + x)^{3}} - \frac{4200xcos(x)}{(cos(x) + x)^{2}} + \frac{1260x^{2}sin(x)}{(cos(x) + x)^{2}} + \frac{140x^{3}cos(x)}{(cos(x) + x)^{2}} - \frac{5x^{4}sin(x)}{(cos(x) + x)^{2}} + \frac{100800x}{(cos(x) + x)^{5}} - \frac{90720x}{(cos(x) + x)^{6}} - \frac{151200x^{2}}{(cos(x) + x)^{6}} - \frac{30240x^{3}}{(cos(x) + x)^{8}} + \frac{90720x^{2}}{(cos(x) + x)^{7}} + \frac{100800x^{3}}{(cos(x) + x)^{7}} - \frac{25200x^{4}}{(cos(x) + x)^{8}} + \frac{30240}{(cos(x) + x)^{5}} - \frac{25200}{(cos(x) + x)^{4}}\\ \end{split}\end{equation} \]