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Problem Let g ( x ) = sin 4 x ln x x 2 g(x)=\dfrac{\sin 4x\;\ln x}{x^{2}} g ( x ) = x 2 sin 4 x ln x g ′ ( x ) g'(x) g ′ ( x ) 4 x ln x cos 4 x − 2 sin 4 x ln x x 3 \dfrac{4x\ln x\cos4x-2\sin4x\ln x}{x^{3}} x 3 4 x ln x cos 4 x − 2 sin 4 x ln x 4 x 2 ln x cos 4 x + sin 4 x − 2 sin 4 x ln x x 4 \dfrac{4x^{2}\ln x\cos4x+\sin4x-2\sin4x\ln x}{x^{4}} x 4 4 x 2 ln x cos 4 x + sin 4 x − 2 sin 4 x ln x 4 x ln x cos 4 x + sin 4 x − 2 sin 4 x ln x x 3 \dfrac{4x\ln x\cos4x+\sin4x-2\sin4x\ln x}{x^{3}} x 3 4 x ln x cos 4 x + sin 4 x − 2 sin 4 x ln x x ln x cos 4 x + sin 4 x − 2 sin 4 x ln x x 3 \dfrac{x\ln x\cos4x+\sin4x-2\sin4x\ln x}{x^{3}} x 3 x ln x cos 4 x + sin 4 x − 2 sin 4 x ln x Browse the problem library