Question
Find \( d y / d x \) for \( 3 x^{2}-y^{2}=4 \) Type answer \( y^{\prime}= \) (numerator)/(denominator) A
Ask by Wade Carroll. in the United States
Mar 17,2025
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Answer
\( y^{\prime} = \frac{3x}{y} \)
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First, we'll differentiate both sides of the equation \( 3x^2 - y^2 = 4 \) with respect to \( x \). Using implicit differentiation, we get: \( 6x - 2y \frac{dy}{dx} = 0 \). Now, solving for \( \frac{dy}{dx} \): \( 2y \frac{dy}{dx} = 6x \) \( \frac{dy}{dx} = \frac{6x}{2y} \) So, \( y' = \frac{6x}{2y} = \frac{3x}{y} \). Final answer: \( y' = \frac{3x}{y} \).