For the curve defined implicitly by

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

Problem

x^{2}y + y^{2} = 10

, which of the following expressions equals

\dfrac{dy}{dx}

in terms of

x

and

y

? (a)

-\dfrac{2y}{x^{2}+2y}

(b)

-\dfrac{2xy}{x^{2}+2y}

(c)

-\dfrac{2xy}{x^{2}}

(d)

-\dfrac{x^{2}+2y}{2xy}

Related theory

Advanced Differentiation
Implicit and Parametric Differentiation
Derivatives of implicit functions
Continuity and Differentiability

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