Let for . Which of the following is…

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

Problem

Let g(x)=(ln⁡x)2e3xg(x)=\dfrac{(\ln x)^{2}}{e^{3x}} for x>0x>0. Which of the following is g′(x)g'(x) simplified? (a) e−3x(2ln⁡xx+3(ln⁡x)2)e^{-3x}\left(\dfrac{2\ln x}{x}+3(\ln x)^{2}\right) (b) e−3x(2x−3ln⁡x)e^{-3x}\left(\dfrac{2}{x}-3\ln x\right) (c) e−3x(2ln⁡xx−3(ln⁡x)2)e^{-3x}\left(\dfrac{2\ln x}{x}-3(\ln x)^{2}\right) (d) e−3x(2ln⁡xx−3ln⁡x)e^{-3x}\left(\dfrac{2\ln x}{x}-3\ln x\right)

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