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

Problem

If y=(x2+1)x2y=(x^{2}+1)^{x^{2}}, then dydx\dfrac{dy}{dx} equals (a) (x2+1)x2[2x ln⁡(x2+1)−2x3x2+1](x^{2}+1)^{x^{2}}\left[2x\,\ln(x^{2}+1)-\dfrac{2x^{3}}{x^{2}+1}\right] (b) (x2+1)x2[2x ln⁡(x2+1)+2xx2+1](x^{2}+1)^{x^{2}}\left[2x\,\ln(x^{2}+1)+\dfrac{2x}{x^{2}+1}\right] (c) (x2+1)x2[2x ln⁡(x2+1)+2x3x2+1](x^{2}+1)^{x^{2}}\left[2x\,\ln(x^{2}+1)+\dfrac{2x^{3}}{x^{2}+1}\right] (d) (x2+1)x2[x ln⁡(x2+1)+2x3x2+1](x^{2}+1)^{x^{2}}\left[x\,\ln(x^{2}+1)+\dfrac{2x^{3}}{x^{2}+1}\right]

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