find $\frac{d y}{d x}$ if $x^{2} + y^{2} = 4$

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Solution

$x^{2} + y^{2} = 4 2 x + 2 y \frac{d y}{d x} = 0 x + y \frac{d y}{d x} = 0 y \frac{d y}{d x} = - x \frac{d y}{d x} = \frac{- x}{y}$

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