AP Calculus ABhardmcq1 pt

If $4x^2+9y^2=36$ defines $y$ implicitly as a function of $x$ , then $\dfrac{d^2y}{dx^2}=$

-\dfrac{4x}{9y}

-\dfrac{4}{9y}

-\dfrac{16}{9y^3}

-\dfrac{16}{9y}

Explanation

Core Concept

First, $\frac{dy}{dx}=-\frac{4x}{9y}$ . Differentiate to get $-\frac{4}{9}\cdot\frac{y-x\frac{dy}{dx}}{y^2}$ , substitute $-\frac{4x}{9y}$ , and use $4x^2+9y^2=36$ . The numerator becomes $4x^2+9y^2=36$ , giving $-\frac{16}{9y^3}$ .

Correct Answer

C $-\dfrac{16}{9y^3}$

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If 4x2+9y2=364x^2+9y^2=364x2+9y2=36 defines yyy implicitly as a function of xxx, then d2ydx2=\dfrac{d^2y}{dx^2}=dx2d2y​=

Explanation

Core Concept

Correct Answer

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

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