If , then has the value equal…

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

Problem

If y=tan⁡xtan⁡2xtan⁡3xy = \tan x \tan 2x \tan 3x , then dydx\frac{dy}{dx} has the value equal to (1) 3sec⁡23xtan⁡xtan⁡2x+sec⁡2xtan⁡2xtan⁡3x+2sec⁡22xtan⁡3xtan⁡x3 \sec^2 3x \tan x \tan 2x + \sec^2 x \tan 2x \tan 3x + 2 \sec^2 2x \tan 3x \tan x (2) 2y(csc⁡2x+2csc⁡4x+3csc⁡6x)2y (\csc 2x + 2 \csc 4x + 3 \csc 6x) (3) 3sec⁡23x−2sec⁡22x−sec⁡2x3 \sec^2 3x - 2 \sec^2 2x - \sec^2 x (4) sec⁡2x+2sec⁡22x+3sec⁡23x\sec^2 x + 2 \sec^2 2x + 3 \sec^2 3x

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