Given-f-x-7-cos-2x-2sin-2-x-find-f-10-x-

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

G i v e n f (x) = 7 + \cos 2 x + 2 \sin^{2} x

f i n d f^{(10)} (x) ?

Commented by bemath last updated on 17/Sep/20

f (x) = 7 + 1 - 2 \sin^{2} x + 2 \sin^{2} x

f (x) = 8 \Rightarrow f^{(10)} (x) = 0

Answered by Olaf last updated on 17/Sep/20

f (x) = 7 + \cos 2 x + {2 \sin}^{2} x

f (x) = 7 + \cos 2 x + 2 \frac{1 - \cos 2 x}{2}

f (x) = 8

f^{(k)} (x) = 0

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

Since \cos 2 x = 1 - {2 \sin}^{2} x, \cos 2 x + {2 \sin}^{2} x

= 1 \Rightarrow f (x) = 7 + \cos 2 x + {2 \sin}^{2} x = 8

\Rightarrow f^{'} (x) = 0 \Rightarrow f^{(n)} (x) = 0 \forall n ⩾ 1, n \in N