AP

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

Problem

If y=tan⁡−1(x1/3+a1/31−x1/3a1/3)y = \tan^{-1} \left( \frac{x^{1/3} + a^{1/3}}{1 - x^{1/3} a^{1/3}} \right) , then dydx=\frac{dy}{dx} = (a) 13x2/3(1+x2/3)\frac{1}{3x^{2/3}(1+x^{2/3})} (b) a3x2/3(1+x2/3)\frac{a}{3x^{2/3}(1+x^{2/3})} (c) −13x2/3(1+x2/3)-\frac{1}{3x^{2/3}(1+x^{2/3})} (d) −a3x2/3(1+x2/3)-\frac{a}{3x^{2/3}(1+x^{2/3})}

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