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Problem Let g ( x ) = ( ln x ) 2 e 3 x g(x)=\dfrac{(\ln x)^{2}}{e^{3x}} g ( x ) = e 3 x ( ln x ) 2 x > 0 x>0 x > 0 g ′ ( x ) g'(x) g ′ ( x ) e − 3 x ( 2 ln x x + 3 ( ln x ) 2 ) e^{-3x}\left(\dfrac{2\ln x}{x}+3(\ln x)^{2}\right) e − 3 x ( x 2 ln x + 3 ( ln x ) 2 ) e − 3 x ( 2 x − 3 ln x ) e^{-3x}\left(\dfrac{2}{x}-3\ln x\right) e − 3 x ( x 2 − 3 ln x ) e − 3 x ( 2 ln x x − 3 ( ln x ) 2 ) e^{-3x}\left(\dfrac{2\ln x}{x}-3(\ln x)^{2}\right) e − 3 x ( x 2 ln x − 3 ( ln x ) 2 ) e − 3 x ( 2 ln x x − 3 ln x ) e^{-3x}\left(\dfrac{2\ln x}{x}-3\ln x\right) e − 3 x ( x 2 ln x − 3 ln x ) Browse the problem library