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MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem Calculate d d x ( x 3 x 2 + 1 ) \dfrac{d}{dx}\left(\dfrac{x^{3}}{x^{2}+1}\right) d x d ( x 2 + 1 x 3 ) .
(a) 3 x 2 ( x 2 + 1 ) − 2 x 3 ( x 2 + 1 ) 2 \dfrac{3x^{2}(x^{2}+1)-2x^{3}}{(x^{2}+1)^{2}} ( x 2 + 1 ) 2 3 x 2 ( x 2 + 1 ) − 2 x 3
(b) 3 x 4 + 2 x 3 ( x 2 + 1 ) 2 \dfrac{3x^{4}+2x^{3}}{(x^{2}+1)^{2}} ( x 2 + 1 ) 2 3 x 4 + 2 x 3
(c) x 4 + 3 x 2 ( x 2 + 1 ) 2 \dfrac{x^{4}+3x^{2}}{(x^{2}+1)^{2}} ( x 2 + 1 ) 2 x 4 + 3 x 2
(d) x 4 + 3 x 2 x 2 + 1 \dfrac{x^{4}+3x^{2}}{x^{2}+1} x 2 + 1 x 4 + 3 x 2
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