Let for . Which of the following expresses…

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

Problem

Let g(x)=(ln⁡x) csc⁡xg(x)= (\ln x)\,\csc x for x>0x>0. Which of the following expresses g′(x)g'(x)? (a) csc⁡xx−(ln⁡x)sec⁡xtan⁡x\displaystyle \frac{\csc x}{x}-(\ln x)\sec x\tan x (b) csc⁡xx+(ln⁡x)csc⁡xcot⁡x\displaystyle \frac{\csc x}{x}+(\ln x)\csc x\cot x (c) csc⁡xx−(ln⁡x)csc⁡xcot⁡x\displaystyle \frac{\csc x}{x}-(\ln x)\csc x\cot x (d) csc⁡xx−(ln⁡x)csc⁡xtan⁡x\displaystyle \frac{\csc x}{x}-(\ln x)\csc x\tan x

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