If y = cos ⁡ x cos ⁡ 2 x cos ⁡ 4 x cos ⁡ 8 x , then d y d x at x = π 2 is

Question

If y = cos ⁡ x cos ⁡ 2 x cos ⁡ 4 x cos ⁡ 8 x , then d y d x at x = π 2 is, 1, 0, 4, 16

MARKS App · Accepted Answer

y = sin ⁡ 16 x 16 sin ⁡ x ∵ cos ⁡ A cos ⁡ 2 A . . . . . . . . . cos ⁡ 2 n - 1 A = sin 2 n A 2 n sin ⁡ A So, d y d x = 1 16 sin ⁡ x ⋅ 16 cos ⁡ 16 x - sin ⁡ 16 x cos ⁡ x sin ⁡ x 2 Putting x = π 2 , we get, d y d x = 1 16 ⋅ 1.16 1 - 0 1 2 = 1

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