The equation defines implicitly as a function of

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

Problem

The equation xey=4x e^{y} = 4 defines yy implicitly as a function of xx. What is dydx\dfrac{dy}{dx} at the point (2,ln⁡2)(2,\ln 2)? (a) −14-\dfrac{1}{4} (b) 12\dfrac{1}{2} (c) −12-\dfrac{1}{2} (d) −12ln⁡2-\dfrac{1}{2\ln 2}

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