Question 460227
Find the fourth derivative by finding all the other derivatives using the chain rule (there is a pattern).


*[tex \LARGE f^'(x) = -n \sin(nx)]


*[tex \LARGE f^{''}(x) = -n^2 \cos(nx)]


*[tex \LARGE f^{'''}(x) = n^3 \sin (nx)]


*[tex \LARGE f^{(4)} (x) = n^4 \cos (nx)]


At x = pi/n,


*[tex \LARGE f^{(4)} (\frac{\pi}{n}) = n^4 \cos (\pi) = -n^4]