For the implicitly defined curve

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

Problem

For the implicitly defined curve exy=x+ye^{xy}=x+y, determine dydx\dfrac{dy}{dx} in terms of xx and yy. (a) 1−exyy1−exyx\displaystyle\frac{1-e^{xy}y}{1-e^{xy}x} (b) 1−exyyexyx−1\displaystyle\frac{1-e^{xy}y}{e^{xy}x-1} (c) exy(1−y)exyx−1\displaystyle\frac{e^{xy}(1-y)}{e^{xy}x-1} (d) 1−yx−1\displaystyle\frac{1-y}{x-1}

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