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JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1
If f(x)=cos⁡x.cos⁡2x.cos⁡4x.cos⁡8x.cos⁡16x,f\left( x \right) = \cos x.\cos 2x.\cos 4x.\cos 8x.\cos 16x, then the value of f′(π4)f'\left( {\frac{\pi }{4}} \right) is
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Correct option: B
2\sqrt 2
Option B (2\sqrt 2) is correct because after simplifying the function using trigonometric identities and then differentiating, the value of f'(π4\frac{\pi}{4}) is 2\sqrt 2.

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