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 5 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 5th\ derivative\ of\ function\ \frac{2ph{c}^{2}}{({x}^{5}({e}^{(\frac{hc}{ktx})} - 1))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2phc^{2}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})}\\\\ &\color{blue}{The\ 5th\ derivative\ of\ function:} \\=&\frac{-750000phc^{2}x^{20}{e}^{(\frac{5hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}} + \frac{3750000phc^{2}x^{20}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}} + \frac{1200000phc^{2}x^{15}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}} - \frac{7500000phc^{2}x^{20}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}} + \frac{7500000phc^{2}x^{20}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}} - \frac{4800000phc^{2}x^{15}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}} - \frac{540000phc^{2}x^{10}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}} + \frac{750000ph^{2}c^{3}x^{19}{e}^{(\frac{5hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}kt} + \frac{4500000ph^{2}c^{3}x^{19}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}kt} + \frac{7200000phc^{2}x^{15}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}} - \frac{1200000ph^{2}c^{3}x^{14}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}kt} - \frac{3600000ph^{2}c^{3}x^{14}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}kt} - \frac{3000000ph^{2}c^{3}x^{19}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}kt} + \frac{3600000ph^{2}c^{3}x^{14}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}kt} + \frac{1620000phc^{2}x^{10}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}} - \frac{1080000ph^{2}c^{3}x^{9}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}kt} + \frac{60000phc^{2}x^{5}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}} - \frac{300000ph^{3}c^{4}x^{18}{e}^{(\frac{5hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{2}t^{2}} + \frac{60000ph^{4}c^{5}x^{17}{e}^{(\frac{5hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{3}t^{3}} + \frac{900000ph^{3}c^{4}x^{18}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{2}t^{2}} + \frac{492000ph^{3}c^{4}x^{13}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{2}t^{2}} + \frac{540000ph^{2}c^{3}x^{9}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}kt} - \frac{6000ph^{5}c^{6}x^{16}{e}^{(\frac{5hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{4}t^{4}} - \frac{120000ph^{4}c^{5}x^{17}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{3}t^{3}} - \frac{103200ph^{4}c^{5}x^{12}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{3}t^{3}} - \frac{1044000ph^{3}c^{4}x^{13}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{2}t^{2}} - \frac{228600ph^{3}c^{4}x^{8}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}k^{2}t^{2}} - \frac{60000ph^{2}c^{3}x^{4}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}kt} - \frac{900000ph^{3}c^{4}x^{18}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{2}t^{2}} - \frac{3000000ph^{2}c^{3}x^{19}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}kt} + \frac{612000ph^{3}c^{4}x^{13}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{2}t^{2}} - \frac{3750000phc^{2}x^{20}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}} - \frac{4800000phc^{2}x^{15}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}} + \frac{1200000ph^{2}c^{3}x^{14}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}kt} - \frac{1620000phc^{2}x^{10}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}} + \frac{540000ph^{2}c^{3}x^{9}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}kt} + \frac{11040ph^{5}c^{6}x^{11}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{4}t^{4}} + \frac{139200ph^{4}c^{5}x^{12}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{3}t^{3}} - \frac{120000phc^{2}x^{5}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}} + \frac{60000ph^{2}c^{3}x^{4}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}kt} + \frac{51240ph^{4}c^{5}x^{7}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}k^{3}t^{3}} - \frac{6060ph^{5}c^{6}x^{6}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}k^{4}t^{4}} - \frac{240phc^{2}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{2}} + \frac{240ph^{2}c^{3}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{2}ktx} + \frac{26640ph^{3}c^{4}x^{3}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}k^{2}t^{2}} - \frac{120ph^{3}c^{4}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{2}k^{2}t^{2}x^{2}} + \frac{291600ph^{3}c^{4}x^{8}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}k^{2}t^{2}} - \frac{6640ph^{4}c^{5}x^{2}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}k^{3}t^{3}} - \frac{38400ph^{4}c^{5}x^{7}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}k^{3}t^{3}} + \frac{240ph^{6}c^{7}x^{15}{e}^{(\frac{5hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{5}t^{5}} + \frac{6000ph^{5}c^{6}x^{16}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{4}t^{4}} - \frac{480ph^{6}c^{7}x^{10}{e}^{(\frac{4hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{5}t^{5}} + \frac{60000ph^{4}c^{5}x^{17}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{3}t^{3}} - \frac{7200ph^{5}c^{6}x^{11}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{4}t^{4}} + \frac{300ph^{6}c^{7}x^{5}{e}^{(\frac{3hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}k^{5}t^{5}} + \frac{300000ph^{3}c^{4}x^{18}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}k^{2}t^{2}} - \frac{36000ph^{4}c^{5}x^{12}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{3}t^{3}} - \frac{63000ph^{3}c^{4}x^{8}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}k^{2}t^{2}} + \frac{2100ph^{5}c^{6}x^{6}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}k^{4}t^{4}} - \frac{13200ph^{3}c^{4}x^{3}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}k^{2}t^{2}} + \frac{1600ph^{4}c^{5}x^{2}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}k^{3}t^{3}} + \frac{940ph^{5}c^{6}x{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}k^{4}t^{4}} - \frac{60ph^{6}c^{7}{e}^{(\frac{2hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}k^{5}t^{5}} + \frac{750000ph^{2}c^{3}x^{19}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}kt} - \frac{60000ph^{3}c^{4}x^{13}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}k^{2}t^{2}} + \frac{3000ph^{4}c^{5}x^{7}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}k^{3}t^{3}} - \frac{100ph^{5}c^{6}x{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}k^{4}t^{4}} + \frac{40ph^{4}c^{5}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{2}k^{3}t^{3}x^{3}} - \frac{10ph^{5}c^{6}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{2}k^{4}t^{4}x^{4}} + \frac{2ph^{6}c^{7}{e}^{(\frac{hc}{ktx})}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{2}k^{5}t^{5}x^{5}} + \frac{750000phc^{2}x^{20}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{6}} + \frac{1200000phc^{2}x^{15}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{5}} + \frac{540000phc^{2}x^{10}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{4}} + \frac{60000phc^{2}x^{5}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{3}} + \frac{240phc^{2}}{(x^{5}{e}^{(\frac{hc}{ktx})} - x^{5})^{2}}\\ \end{split}\end{equation} \]