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MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem Determine d d x [ ( x 2 + 1 ) 5 sin 3 x ( 3 x − 4 ) 2 ] \dfrac{d}{dx}\!\left[\dfrac{(x^{2}+1)^{5}\sin^{3}x}{(3x-4)^{2}}\right] d x d [ ( 3 x − 4 ) 2 ( x 2 + 1 ) 5 sin 3 x ] ( x 2 + 1 ) 5 sin 3 x ( 3 x − 4 ) 2 ( 5 x x 2 + 1 + 3 cot x − 6 3 x − 4 ) \displaystyle \frac{(x^{2}+1)^{5}\sin^{3}x}{(3x-4)^{2}}\left(\frac{5x}{x^{2}+1}+3\cot x-\frac{6}{3x-4}\right) ( 3 x − 4 ) 2 ( x 2 + 1 ) 5 sin 3 x ( x 2 + 1 5 x + 3 cot x − 3 x − 4 6 ) ( x 2 + 1 ) 5 sin 3 x ( 3 x − 4 ) 2 ( 10 x x 2 + 1 + 3 tan x − 6 3 x − 4 ) \displaystyle \frac{(x^{2}+1)^{5}\sin^{3}x}{(3x-4)^{2}}\left(\frac{10x}{x^{2}+1}+3\tan x-\frac{6}{3x-4}\right) ( 3 x − 4 ) 2 ( x 2 + 1 ) 5 sin 3 x ( x 2 + 1 10 x + 3 tan x − 3 x − 4 6 ) ( x 2 + 1 ) 5 sin 3 x ( 3 x − 4 ) 2 ( 10 x x 2 + 1 + 3 cot x − 6 3 x − 4 ) \displaystyle \frac{(x^{2}+1)^{5}\sin^{3}x}{(3x-4)^{2}}\left(\frac{10x}{x^{2}+1}+3\cot x-\frac{6}{3x-4}\right) ( 3 x − 4 ) 2 ( x 2 + 1 ) 5 sin 3 x ( x 2 + 1 10 x + 3 cot x − 3 x − 4 6 ) ( x 2 + 1 ) 5 sin 3 x ( 3 x − 4 ) 2 ( 10 x x 2 + 1 + 3 cot x + 6 3 x − 4 ) \displaystyle \frac{(x^{2}+1)^{5}\sin^{3}x}{(3x-4)^{2}}\left(\frac{10x}{x^{2}+1}+3\cot x+\frac{6}{3x-4}\right) ( 3 x − 4 ) 2 ( x 2 + 1 ) 5 sin 3 x ( x 2 + 1 10 x + 3 cot x + 3 x − 4 6 ) Browse the problem library