Math  /  Algebra

QuestionFind dydx\frac{d y}{d x} by implicit differentiation, if x2+y2=4x^{2}+y^{2}=4, dydx=\frac{d y}{d x}= \square

Studdy Solution
Solve for dydx\frac{dy}{dx}. First, isolate the term involving dydx\frac{dy}{dx}:
2ydydx=2x2y \cdot \frac{dy}{dx} = -2x
Next, divide both sides by 2y 2y to solve for dydx\frac{dy}{dx}:
dydx=2x2y\frac{dy}{dx} = \frac{-2x}{2y}
Simplify the expression:
dydx=xy\frac{dy}{dx} = \frac{-x}{y}
The derivative dydx\frac{dy}{dx} is:
xy\boxed{\frac{-x}{y}}

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