Use implicit differentiation to determine $\frac { d y } { d x }$ where xy + 10 = $x ^ { 2 }$ . Is $\frac { d y } { d x } = \frac { 2 x - y } { x }$ correct?

Question

Quizplus · Accepted Answer

Differentiating both sides of the equation $xy + 10 = x^2$ with respect to $x$ gives $y + x\frac{dy}{dx} = 2x$. Solving for $\frac{dy}{dx}$ yields $\frac{dy}{dx} = \frac{2x - y}{x}$, confirming the given expression is correct.

Use Implicit Differentiation to Determine dydx\frac { d y } { d x }dxdy​

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