Which of the following is an equivalent expression for the fourth derivative of ?

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Which of the following is an equivalent expression for the fourth derivative of f(x)=tan⁡xf(x)=\tan x? (a) 4sec⁡2xtan⁡x(tan⁡2x+2sec⁡2x)4\sec^{2}x\tan x\left(\tan^{2}x+2\sec^{2}x\right) (b) 8sec⁡2xtan⁡x(tan⁡2x+2sec⁡2x)8\sec^{2}x\tan x\left(\tan^{2}x+2\sec^{2}x\right) (c) 8sec⁡xtan⁡x(tan⁡2x+2sec⁡2x)8\sec x\tan x\left(\tan^{2}x+2\sec^{2}x\right) (d) 8sec⁡2xtan⁡x(tan⁡2x+sec⁡2x)8\sec^{2}x\tan x\left(\tan^{2}x+\sec^{2}x\right)

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