Apentix/AP Calculus AB/Unit 3: Differentiation: Composite, Implicit, and Inverse Functions/Question
AP Calculus ABmediummcq1 pt

If ey+xy=2e^y+xy=2 defines yy implicitly as a function of xx, then dydx=\dfrac{dy}{dx}=

A.−yey+1-\dfrac{y}{e^y+1}
B.−yey+x-\dfrac{y}{e^y+x}
C.yey+x\dfrac{y}{e^y+x}
D.ey+xy\dfrac{e^y+x}{y}

Explanation

Core Concept

Differentiating gives eydydx+y+xdydx=0e^y\frac{dy}{dx}+y+x\frac{dy}{dx}=0. Factoring and solving gives dydx=−yey+x\frac{dy}{dx}=-\frac{y}{e^y+x}.

Correct Answer

B−yey+x-\dfrac{y}{e^y+x}

More Unit 3: Differentiation: Composite, Implicit, and Inverse Functions practice questions

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 3: Differentiation: Composite, Implicit, and Inverse Functions Questions →