If , , , and , then…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

If u=f(x3)u = f(x^3), v=g(x2)v = g(x^2), f′(x)=cos⁡xf'(x) = \cos x, and g′(x)=sin⁡xg'(x) = \sin x, then dudv\frac{du}{dv} is (a) 32xcos⁡x3csc⁡x2\frac{3}{2} x \cos x^3 \csc x^2 (b) 23sin⁡x3sec⁡x2\frac{2}{3} \sin x^3 \sec x^2 (c) tan⁡x\tan x (d) none of these

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