# How do you implicitly differentiate # (x^2)/9+(x-y^2)/6=1 #?

I found:

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To implicitly differentiate the given equation, apply the rules of implicit differentiation:

[ \frac{d}{dx}\left(\frac{x^2}{9} + \frac{x-y^2}{6}\right) = \frac{d}{dx}(1) ]

[ \frac{2x}{9} + \frac{1}{6}\left(\frac{d}{dx}(x) - \frac{d}{dx}(y^2)\right) = 0 ]

[ \frac{2x}{9} + \frac{1}{6}(1 - 2y\frac{dy}{dx}) = 0 ]

Solve for (\frac{dy}{dx}) to get the implicit derivative.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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