AP Calculus ABmediummcq1 pt

If $x^2y+y^2=10$ defines $y$ implicitly as a function of $x$ , then $\dfrac{dy}{dx}=$

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

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

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

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

Explanation

Core Concept

Differentiate using the product rule on $x^2y$ to get $2xy+x^2\frac{dy}{dx}+2y\frac{dy}{dx}=0$ . Solving for $\frac{dy}{dx}$ gives $-\frac{2xy}{x^2+2y}$ .

Correct Answer

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

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

hardIf $f(x)=\sin(\cos(x^2))$, then $f'(x)=$
hardIf $f(x)=\arctan x$, then $f''(x)=$
hardIf $f(x)=e^{2x}\sin x$, then $f''(x)=$
hardIf $f(x)=\sqrt{e^{2x}+1}$, then $f'(x)=$
hardIf $f(x)=\sin^2(\cos x)$, then $f'(x)=$

Try a random question →

Practice more AP Calculus AB questions with full explanations

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

If x2y+y2=10x^2y+y^2=10x2y+y2=10 defines yyy implicitly as a function of xxx, then dydx=\dfrac{dy}{dx}=dxdy​=

Explanation

Core Concept

Correct Answer

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

If $x^2y+y^2=10$ defines $y$ implicitly as a function of $x$ , then $\dfrac{dy}{dx}=$