Apentix/AP Calculus AB/Unit 5: Analytical Applications of Differentiation/Question

AP Calculus ABhardmcq1 pt

For the curve $x^3+y^3=6xy$ , what is $\dfrac{dy}{dx}$ ?

A.

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

B.

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

C.

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

D.

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

Explanation

Core Concept

Differentiating gives $3x^2+3y^2\cdot y'=6y+6x\cdot y'$ . Rearranging, $(3y^2-6x)y'=6y-3x^2$ , and dividing by 3 gives $(y^2-2x)y'=2y-x^2$ .

Correct Answer

C $\dfrac{2y-x^2}{y^2-2x}$

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