Question Number 114066 by john santu last updated on 17/Sep/20

Given f(x)=7+cos 2x+2sin ^2 x find f^((10)) (x) ?

Commented bybemath last updated on 17/Sep/20

f(x)=7+1−2sin ^2 x+2sin ^2 x f(x)=8 ⇒f ^((10)) (x)= 0

Answered by Olaf last updated on 17/Sep/20

f(x) = 7+cos2x+2sin^2 x f(x) = 7+cos2x+2((1−cos2x)/2) f(x) = 8 f^((k)) (x) = 0

Answered by 1549442205PVT last updated on 17/Sep/20

Since cos2x=1−2sin^2 x,cos2x+2sin^2 x =1⇒f(x)=7+cos2x+2sin^2 x=8 ⇒f ′(x)=0⇒f^((n)) (x)=0∀n≥1,n∈N