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Calculus Level 4

Evaluate d d [ sin ⁡ x ] [ sin ⁡ ( 2016 x ) ] ∣ x = 2 π \left. \dfrac{d}{d \left[ \sin x \right] } \left[ \sin \left(2016x \right) \right] \right|_{x = 2\pi } .

Bonus: How'd I come up with the title?

Credit: A suggestion by the challenge master on the solution to a similar problem.


The answer is 2016.

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Hobart Pao by Hobart Pao , 23, USA

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1 solution

Akhil Bansal
Feb 8, 2016

d ( sin ⁡ 2016 x ) d ( sin ⁡ x ) = d ( sin ⁡ 2016 x ) d x × d x d sin ⁡ ( x ) = 2016 × cos ⁡ ( x ) cos ⁡ ( x ) = 2016 \large \dfrac{d(\sin 2016x)}{d(\sin x)} = \dfrac{d(\sin 2016x)}{dx} \times \dfrac{dx}{d\sin(x)} = \dfrac{2016 \times \cos(x)}{\cos(x)} = 2016

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