A Level

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Determine ddx[(x+3)sec⁡x−xcos⁡x2x]\dfrac{d}{dx}\left[\dfrac{(x+3)\sec x - x\cos x}{2x}\right]. (a) sec⁡x+(x+3)sec⁡xtan⁡x−cos⁡x+xsin⁡x2x\dfrac{\sec x + (x+3)\sec x\tan x - \cos x + x\sin x}{2x} (b) (sec⁡x+(x+3)sec⁡xtan⁡x−cos⁡x−xsin⁡x)(2x)−2((x+3)sec⁡x−xcos⁡x)(2x)2\dfrac{\bigl(\sec x + (x+3)\sec x\tan x - \cos x - x\sin x\bigr)(2x) - 2\bigl((x+3)\sec x - x\cos x\bigr)}{(2x)^2} (c) (sec⁡x+(x+3)sec⁡xtan⁡x−cos⁡x+xsin⁡x)(2x)−2((x+3)sec⁡x−xcos⁡x)(2x)2\dfrac{\bigl(\sec x + (x+3)\sec x\tan x - \cos x + x\sin x\bigr)(2x) - 2\bigl((x+3)\sec x - x\cos x\bigr)}{(2x)^2} (d) sec⁡x+(x+3)sec⁡xtan⁡x−cos⁡x+xsin⁡x2x  −  (x+3)sec⁡x−xcos⁡xx2\dfrac{\sec x + (x+3)\sec x\tan x - \cos x + x\sin x}{2x}\; -\; \dfrac{(x+3)\sec x - x\cos x}{x^{2}}

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