Use implicit differentiation to determine $\frac{d y}{d x}$
where $x ^ { 2 }$ + $y ^ { 2 }$ = 4. Is $\frac { d y } { d x } = \frac { x } { y }$ correct?

Question

Use implicit differentiation to determine $\frac{d y}{d x}$
 where $x ^ { 2 }$ + $y ^ { 2 }$ = 4. Is $\frac { d y } { d x } = \frac { x } { y }$ correct?

Quizplus · Accepted Answer

Differentiating both sides of $x^2 + y^2 = 4$ with respect to $x$ using implicit differentiation gives $2x + 2y\frac{dy}{dx} = 0$. Solving for $\frac{dy}{dx}$ yields $\frac{dy}{dx} = -\frac{x}{y}$, not $\frac{x}{y}$.

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Use Implicit Differentiation to Determine $\frac{d y}{d x}$ Where $x ^ { 2 }$