$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$ $x ^ { 2 } + y ^ { 2 } = 25$
A) $\frac { d y } { d x } = \frac { x } { y }$
B) $\frac { d y } { d x } = - \frac { x } { y }$
C) $\frac { d y } { d x } = \frac { y } { x }$
D) $\frac { d y } { d x } = - \frac { y } { x }$
E) $\frac { d y } { d x } = - \frac { x } { y ^ { 2 } }$

Question

Quizplus · Accepted Answer

Differentiating both sides of $x^2 + y^2 = 25$ with respect to $x$ gives $2x + 2y\frac{dy}{dx} = 0$. Solving for $\frac{dy}{dx}$ yields $\frac{dy}{dx} = -\frac{x}{y}$.

Find dydx by implicit differentiation. \text { Find } \frac { d y } { d x } \text { by implicit differentiation. } Find dxdy​ by implicit differentiation.

$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$