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If f(x) = cosx• cos2x •cos4x• cos8x• cos16x , then find derivative at x=π/4

If f(x) = cosx• cos2x •cos4x• cos8x• cos16x , then find derivative at x=π/4

Grade:11

1 Answers

Arun
25757 Points
5 years ago
Dear student
 
First check, cos(45) = 1/2^(1/2)
Cos(2*45) = 0
Cos(4*45) = -1
Cos(8*45) = 1
Cos(16*45) = 1
 
f'(x) at pi/4
 Only one term is left
-2sin 2x cosx cos4x cos8x cos16x
At x = pi/4
= -2 sin90 cos 45 cos 180 cos360 cos720
= -2*[1/2^(1/2)]* (-1)*1*1
= \sqrt2
 
Regards
Arun (askIITians forum expert)

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