For , let . Which of the following equals…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

For x>0x>0, let g(x)=ln⁡xe3xg(x)=\dfrac{\ln x}{e^{3x}}. Which of the following equals g′(x)g'(x)? (a) 1x+3ln⁡xe3x\displaystyle \frac{\frac{1}{x}+3\ln x}{e^{3x}} (b) 1x−ln⁡xe3x\displaystyle \frac{\frac{1}{x}-\ln x}{e^{3x}} (c) 1x−3ln⁡xe3x\displaystyle \frac{\frac{1}{x}-3\ln x}{e^{3x}} (d) 1x−3ln⁡xe6x\displaystyle \frac{\frac{1}{x}-3\ln x}{e^{6x}}

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