Let . Which of the following expressions equals , the third derivative of with…

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

Problem

Let y=cot⁡xy=\cot x. Which of the following expressions equals y(3)y^{(3)}, the third derivative of yy with respect to xx? (a) −4csc⁡2xcot⁡2x+2csc⁡4x-4\csc^{2}x\cot^{2}x+2\csc^{4}x (b) −4csc⁡2xcot⁡2x−2csc⁡4x-4\csc^{2}x\cot^{2}x-2\csc^{4}x (c) 4csc⁡2xcot⁡2x−2csc⁡4x4\csc^{2}x\cot^{2}x-2\csc^{4}x (d) −2csc⁡2xcot⁡2x−4csc⁡4x-2\csc^{2}x\cot^{2}x-4\csc^{4}x

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