Given , what is…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Given h(x)=(x2+1)sec⁡xcot⁡xh(x)=(x^{2}+1)\sec x\cot x, what is h′(x)h'(x)? (a) sec⁡x[2xcot⁡x+(x2+1)]\sec x\left[2x\cot x+(x^{2}+1)\right] (b) sec⁡x[2xcot⁡x+(x2+1)−(x2+1)csc⁡2x]\sec x\left[2x\cot x+(x^{2}+1)-(x^{2}+1)\csc^{2}x\right] (c) sec⁡x[2xcot⁡x+(x2+1)tan⁡x−(x2+1)csc⁡2x]\sec x\left[2x\cot x+(x^{2}+1)\tan x-(x^{2}+1)\csc^{2}x\right] (d) sec⁡x[2xcot⁡x+(x2+1)+(x2+1)csc⁡2x]\sec x\left[2x\cot x+(x^{2}+1)+(x^{2}+1)\csc^{2}x\right]

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