If f x = cos ⁡ x . cos ⁡ 2 x . cos ⁡ 4 x . cos ⁡ 8 x . cos ⁡ 16 x , then f ' π 4 is ( where f ' ( x ) = d dx f ( x ) )

Question

If f x = cos ⁡ x . cos ⁡ 2 x . cos ⁡ 4 x . cos ⁡ 8 x . cos ⁡ 16 x , then f ' π 4 is ( where f ' ( x ) = d dx f ( x ) ), 2, 1 2, 1, None of these

MARKS App · Accepted Answer

f x = 2 sin ⁡ x . cos ⁡ x . cos ⁡ 2 x . cos ⁡ 4 x . cos ⁡ 8 x . cos ⁡ 16 x 2 sin ⁡ x = sin ⁡ 32 x 2 5 sin ⁡ x ∴ f ' x = 1 32 . 32 cos ⁡ 32 x . sin ⁡ x - cos ⁡ x . sin ⁡ 32 x sin 2 ⁡ x ∴ f ' π 4 = 32 . 1 2 - 1 2 . 0 32 . 1 2 2 = 2

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