Question Number 179328 by bekkiyor last updated on 28/Oct/22
$${y}\left({x}\right)={cos}\mathrm{2}{x},\:\:\left(\frac{{d}}{{dx}}{y}\left({x}\right)\right)^{{n}} =\:? \\ $$
Answered by pablo1234523 last updated on 28/Oct/22
$${y}=\mathrm{cos}\:\mathrm{2}{x} \\ $$$$\frac{{dy}}{{dx}}=−\mathrm{2sin}\:\mathrm{2}{x} \\ $$$$\left(\frac{{dy}}{{dx}}\right)^{{n}} =−\mathrm{2}^{{n}} \mathrm{sin}^{{n}} \:\mathrm{2}{x} \\ $$
Commented by DvMc last updated on 28/Oct/22
$${In}\:{the}\:{end}\:{would}\:{be} \\ $$$$\left(−\mathrm{2}\right)^{{n}} {sin}^{{n}} \mathrm{2}{x} \\ $$